1

Warm up

2

3

Homework to check:page 88 #7­12, 25­28, 32­35, 39, 56­58

4

Quick quiz review

2, 5, 9, 14, 20, ...

Make a conjecture about the next number.

5

6

2-3: Conditional Statements

Analyze if­then statements

Write the converse, inverse, and contrapositive of if­then statements

7

Conditional StatementsCan be written in if­then form

Example: If it is raining outside, then you use an umbrella.

The "if" part is called the hypothesis.

The "then" partis called the conclusion.

8

Try it:Identify the hypothesis and conclusion.

If we go to the mall, then I will get a shirt.

9

Example continued...

p: it is raining outside

q: you use an umbrella

if p then q

p q

p implies q

It can be written in a few different ways:

10

We can do three different things with a conditional statement.

1. Find the converse

2. Find the inverse

3. Find the contrapositive

Each of these things has its own truth value.

11

Converseq p

p: it is raining outsideq: you use an umbrella

Conditional p q

Reminder:

You use an umbrella, therefore it is raining.

12

Inverse~p ~q

p: it is raining outsideq: you use an umbrella

Conditional p q

Reminder:

It is not raining outside, therefore you do not use an umbrella.

13

Contrapositive~q ~p

p: it is raining outsideq: you use an umbrella

Conditional p q

Reminder:

You are not using an umbrella, therefore it is not raining outside.

14

Page 93

true

true

true

true

15

Statements can have truth values. Let's try an example:

page 92

16

17

Analyze if­then statements

Write the converse, inverse, and contrapositive of if­then statements

Now you can:

Homework due tomorrow:page 94#1­3, 6­10, 37­42

18

Homework due tomorrow:page 94#1­3, 6­10, 37­42