Warm Up
What is the hypothesis and the
conclusion. If 6x – 5 = 19, then x = 4?
Write in if-then form.
For Example
Truth Values of Conditionals
A. Determine the truth value of the conditional
statement. If true, explain your reasoning. If false,
give a counterexample.
If you subtract a whole number from another whole
number, the result is also a whole number.
Counterexample: 2 – 7 = –5
2 and 7 are whole numbers, but –5 is an integer, not a
whole number.
The conclusion is false.
Answer: Since you can find a counterexample, the
conditional statement is false.
For Example
Truth Values of Conditionals
B. Determine the truth value of the conditional
statement. If true, explain your reasoning. If false,
give a counterexample.
If last month was February, then this month is March.
When the hypothesis is true, the conclusion is also true,
since March is the month that follows February.
Answer: So, the conditional statement is true.
You Try
A. Determine the truth value of the conditional
statement. If true, explain your reasoning. If false,
give a counterexample.
The product of whole numbers is greater than or
equal to 0.
A. True; when the
hypothesis is true, the
conclusion is also true.
B. False; –3 ● 4 = –12
You Try
B. Determine the truth value of the conditional
statement. If true, explain your reasoning. If false,
give a counterexample.
If yesterday was Tuesday, then today is Monday.
A. True; when the
hypothesis is true, the
conclusion is false.
B. False; today is
Wednesday.
Take Note
Converse
Description: When you switch the hypothesis and
conclusion. q → 𝑝
Take Note
Inverse
Description: When you negate both the
hypothesis and conclusion. ~p → ~𝑞
Take Note
Contrapositive
Description: When you switch and negate both
the hypothesis and conclusion. ~q → ~𝑝
Take Note
Example:
If-then: If it’s so hot, then milk is a bad choice
𝒑→𝒒
Converse:
𝒒→𝒑
Inverse:
~𝒑 → ~𝒒
Contrapositive:
~𝒒 → ~𝒑
You Try
Find the Converse, Inverse and Contrapositive. Are they true?
If-then: If you’re a T-Rex, then you hate pushups.
𝒑→𝒒
Converse:
𝒒→𝒑
Inverse:
~𝒑 → ~𝒒
Contrapositive:
~𝒒 → ~𝒑
Homework
• HW 12: Pg.111 #’s 10-14, 16,17, 35, 47,
53-56