More on Conditionals

1
More on Conditionals
2
Objectives

• Write the converse, inverse, and contrapositive
  of a given conditional statement.
• Determine the premise and conclusion of a given
  conditional statement.
• Rewrite a given conditional statement in standard
  if . . ., then . . . form.
• Rewrite a biconditional as the conjunction of two
  conditionals.

3
Objectives

• Determine if two statements are equivalent using
  truth tables.
• Write an equivalent variation of a given
  conditional.

4
Vocabulary

• converse
• inverse
• contrapositive
• only if
• biconditional

5
Conditionals
Name Symbolic Form
Conditional
Converse
Inverse
Contrapositive
6
Using the statements below, write the sentence
representation of each of the symbolic
expressions
p
I am a multimillion-dollar lottery winner.
q
I am a world traveler.
7
Using the statements below, write the sentence
representation of each of the symbolic
expressions
p
I am a multimillion-dollar lottery winner.
q
I am a world traveler.
8
Using the statements below, write the sentence
representation of each of the symbolic
expressions
p
I am a multimillion-dollar lottery winner.
q
I am a world traveler.
9
Using the statements below, write the sentence
representation of each of the symbolic
expressions
p
I am a multimillion-dollar lottery winner.
q
I am a world traveler.
10
Write the converse, inverse, and contrapositive
of the sentence
If you do not eat meat, you are a vegetarian
Converse
If you are a vegetarian, then you do not eat meat.
Inverse
If you do eat meat, then you are not a vegetarian.
Contrapositive
If you are not a vegetarian, then you do eat meat.
11
Write the converse, inverse, and contrapositive
of the sentence
You do not win, if you do not buy a lottery
ticket.
Converse
If you do not win, then you do not buy a lottery
ticket.
Inverse
If you buy a lottery ticket, then you win.
Contrapositive
If you win, then you buy a lottery ticket.
12
Determine the premise and conclusion of the
statement
premise
conclusion
I eat raw fish only if I am in a Japanese
restaurant.
Rewrite the compound statement in standard form.
13
Write the biconditional as a conjunction of two
conditionals
We eat at Burger World if an only if Ju Jus
Kitsch-Inn is closed.
14
Translate the two statements into symbolic form
and use truth tables to determine whether the
statements are equivalent.

1. If I do not have health insurance, I cannot have
   surgery.

1. If I can have surgery, then I do have health
   insurance.

15
Determine which pairs of statements are
equivalent.

1. If Proposition III passes, freeways are improved.
2. If Proposition III is defeated, freeways are not
   improved.
3. If the freeways are not improved, then
   Proposition III does not pass.
4. If the freeways are improved, Proposition III
   passes.