CLASS 1

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CLASS 1
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MATHEMATICAL REASONING
In this chapter we will learn the concept of
logic. Logical thinking is very important for
correct decision making and solving problems in
our daily life.
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4.1 Statement
Look at beautiful flowers over there
Thats amazing
DO NOT STEP ON ROSES
Roses can be found in many colours
Such as red, yellow, and pink.
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4.1 Statement
A statement is a sentences that is either true Or
false but not both
look at the following sentences

• Do not pluck the roses
• Thats amazing
• Looks at the roses over there
• Roses can be found in many colours such
• as red, yellow and pink.

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4.1 Statement
Determine whether each of the following is a
statement or not

• 3 x 2 6
• what is your height?
• An equilateral triangle has sided
• of equal length
• 7 lt 11
• x gt y
• the cube root of 27 is 9
• Run, fire !

Statement
NOT Statement
Statement
Statement
NOT Statement
Statement
NOT Statement
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4.2 Quantifiers All and Some
Quantifiers are words that indicate the number
of objects or cases referred to in a statement.
The quantifier all refer to each and every
object or case
Consider the following statements

• All pentagons have 5 sides.
• Every pentagon has 5 sides.
• Any pentagon has 5 sides.

All three statements means that each and every
pentagon has five sides. Therefore the quantifier
all may be replaced with every or any
based on the context.
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4.2 Quantifiers All and Some
All is used if each if each and every object
has the property stated. Some is used if there
exists one or more objects that do not have the
property stated.
ALL SPIDER HAVE 8 LEGS
Property
Object
See skill practice 4.2d page 85
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4.2 Quantifiers All and Some
The quantifier some refers to one or more
objects or cases
Some may be replaced with several, one of
and part of based on the context.

• Some whole numbers are divisible by 5
• Several whole numbers are divisible by 5
• One of the factors of 4 is also a factor of 5
• Part of a whole is a fraction.

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CLASS 2
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4.3 OPERATION ON STATEMENTS
Operations can be performed on given
statements Using the words

• not or no to negate a statement
• and or or to combine two statement

Negation of a true statement using not or no
results in a false statement and vice versa
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4.3 Negation of a statement
The symbol (tilde) denotes negation. p
denotes negation of p which means not p or no
p
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4.3 Negation of a statement
Operations can be performed on given
statements Using the words

• not or no to negate a statement
• and or or to combine two statement

Negation of a true statement using not or no
results in a false statement and vice versa
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4.3 Negation of a statement
Change the truth value of each of the following
statements using words not or no

• 42 is 16
• 3 2 7
• Universal set is a subset of empty set

Solution

• 42 is not 16
• 3 2 ? 7
• Universal set is not a subset of empty set

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4.3 Negation of a statement
Exercises
Construct statements using not or no to
change the truth value of each of the following
statements
a) Kites have 2 adjacent equal sides.
No kites have 2 adjecent equal sides.
b) Perpendicular lines meet at 90
Perpendicular lines do not meet at 90
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4.3 Negation of a statement
c) -11 - 7 9
-11 7 ? 9

• A reflection on a line is equivalent to a
• rotation of 180

A reflection on a line is not equivalent to a
rotation of 180
e) Factors of 9 are factors of 18.
Factors of 9 are not factors of 18.
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Compound statement using and
A compound statement can be formed from two given
statements using the word and
Example The earth spins on its own axis. The
earth orbits around the sun.
Compound statement The earth spins on its own
axis.
and
The earth orbits around the sun.
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Compound statement using and
Examples
Write two statements from compound statements
112 is 121 and 92 is 81
112 is 121 92 is 81
2 x 5 10 and (8)1/3 ? 2
2 x 5 10 (8)1/3 ? 2
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Compound statement using or
Examples
Write two statements from compound statements
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Truth value of compound statement
Examples
Write two statements from compound statements