Sec. 3.6 Euler Circles and Syllogistic Arguments

1
Sec. 3.6 Euler Circles and Syllogistic Arguments
2
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
3
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
The premise is ALWAYS true
4
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
5
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
6
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All ostriches are birds
All ostriches sing
7
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All ostriches are birds
All ostriches sing
Birds
8
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All ostriches are birds
All ostriches sing
Birds
Sing
9
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All ostriches are birds
All ostriches sing
Birds
Ostriches
Sing
10
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All ostriches are birds
All ostriches sing
Birds
Ostriches
Sing
VALID
11
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All animals with wings can fly
All ostriches are birds
Birds have wings
All ostriches sing
Birds can fly
Birds
Ostriches
Sing
VALID
12
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All animals with wings can fly
All ostriches are birds
Birds have wings
All ostriches sing
Birds can fly
Animals with wings
Birds
Ostriches
Sing
VALID
13
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All animals with wings can fly
All ostriches are birds
Birds have wings
All ostriches sing
Birds can fly
Animals with wings
Birds
Ostriches
Sing
Fly
VALID
14
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All animals with wings can fly
All ostriches are birds
Birds have wings
All ostriches sing
Birds can fly
Animals with wings
Birds
Ostriches
Birds
Sing
Fly
VALID
15
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All birds sing
All animals with wings can fly
All ostriches are birds
Birds have wings
All ostriches sing
Birds can fly
Animals with wings
Birds
Ostriches
Birds
Sing
Fly
VALID
VALID
16
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
Rhinos have wings
Rhinos can fly
17
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
Rhinos have wings
Rhinos can fly
Animals with wings
18
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
Rhinos have wings
Rhinos can fly
Animals with wings
Fly
19
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
Rhinos have wings
Rhinos can fly
Animals with wings
Rhinos
Fly
20
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
Rhinos have wings
Rhinos can fly
Animals with wings
Rhinos
Fly
VALID
21
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
All watermelons are edible
Rhinos have wings
Some edible foods are fruits
Rhinos can fly
All watermelons are fruits
Animals with wings
Rhinos
Fly
VALID
22
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
All watermelons are edible
Rhinos have wings
Some edible foods are fruits
Rhinos can fly
All watermelons are fruits
Animals with wings
Rhinos
Watermelons
Fly
VALID
23
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
All watermelons are edible
Rhinos have wings
Some edible foods are fruits
Rhinos can fly
All watermelons are fruits
Animals with wings
Rhinos
Watermelons
Edible
Fly
VALID
24
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
All watermelons are edible
Rhinos have wings
Some edible foods are fruits
Rhinos can fly
All watermelons are fruits
Animals with wings
Rhinos
Watermelons
Edible
Fly
VALID
Fruits
25
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All animals with wings can fly
All watermelons are edible
Rhinos have wings
Some edible foods are fruits
Rhinos can fly
All watermelons are fruits
Animals with wings
Rhinos
Watermelons
Edible
Fly
VALID
Fruits
26
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All rich people are doctors
All car mechanics are doctors
27
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All rich people are doctors
All car mechanics are doctors
Car mechanics
28
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All rich people are doctors
All car mechanics are doctors
Rich
Car mechanics
29
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All rich people are doctors
All car mechanics are doctors
Rich
Car mechanics
Doctors
30
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All rich people are doctors
All car mechanics are doctors
Rich
Car mechanics
Doctors
VALID
31
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All X's are Y's
All rich people are doctors
Some Y's are Z's
All car mechanics are doctors
Some X's are Z's
Rich
Car mechanics
Doctors
VALID
32
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All X's are Y's
All rich people are doctors
Some Y's are Z's
All car mechanics are doctors
Some X's are Z's
Rich
Car mechanics
Xs
Doctors
VALID
33
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All X's are Y's
All rich people are doctors
Some Y's are Z's
All car mechanics are doctors
Some X's are Z's
Rich
Ys
Car mechanics
Xs
Doctors
VALID
34
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All X's are Y's
All rich people are doctors
Some Y's are Z's
All car mechanics are doctors
Some X's are Z's
Rich
Ys
Car mechanics
Xs
Zs
Doctors
VALID
35
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All car mechanics are rich
All X's are Y's
All rich people are doctors
Some Y's are Z's
All car mechanics are doctors
Some X's are Z's
Rich
Ys
Car mechanics
Xs
Zs
Doctors
VALID
36
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All astronauts can fly
Some pilots are astronauts
37
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All astronauts can fly
Some pilots are astronauts
Pilots
38
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All astronauts can fly
Some pilots are astronauts
Fly
Pilots
39
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All astronauts can fly
Some pilots are astronauts
Fly
Astronauts
Pilots
40
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All astronauts can fly
Some pilots are astronauts
Fly
Astronauts
Pilots
41
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All birds sing
All astronauts can fly
All canaries sing
Some pilots are astronauts
Some canaries are birds
Fly
Astronauts
Pilots
42
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All birds sing
All astronauts can fly
All canaries sing
Some pilots are astronauts
Some canaries are birds
Fly
Astronauts
Birds
Pilots
43
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All birds sing
All astronauts can fly
All canaries sing
Some pilots are astronauts
Some canaries are birds
Sings
Fly
Astronauts
Birds
Pilots
44
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All birds sing
All astronauts can fly
All canaries sing
Some pilots are astronauts
Some canaries are birds
Sings
Fly
Canaries
Astronauts
Birds
Pilots
45
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All pilots can fly
All birds sing
All astronauts can fly
All canaries sing
Some pilots are astronauts
Some canaries are birds
Sings
Fly
Canaries
Astronauts
Birds
Pilots
46
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
No horses can fly
47
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
No horses can fly
Horses
48
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
No horses can fly
Animals with 4 legs
Horses
49
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
No horses can fly
Animals with 4 legs
Can fly
Horses
50
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
No horses can fly
Animals with 4 legs
Can fly
Horses
VALID
51
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
No horses can fly
Horses
Animals with 4 legs
Can fly
Horses
VALID
52
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
Animals with 4 legs
No horses can fly
Horses
Animals with 4 legs
Can fly
Horses
VALID
53
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
Animals with 4 legs
No horses can fly
Horses
Cannot fly
Animals with 4 legs
Can fly
Horses
VALID
54
Sec. 3.6 Euler Circles and Syllogistic Arguments
Def Deductive reasoning is the process of using
logic to reason to a necessary and
inescapable conclusion from a given set
of premises
An argument is VALID if the conclusion is ALWAYS
true
The premise is ALWAYS true
Determine whether the following arguments are
valid or invalid.
All horses have 4 legs
No animals with four legs can fly
Animals with 4 legs
No horses can fly
Horses
Cannot fly
Animals with 4 legs
Can fly
Horses
VALID
VALID