2-3 Conditional Statements- Related

What are the three related conditional

statements?

How are the three related conditional statements made?

• Analyze statements in if-then form.

• Write the converse, inverse, and contrapositive of if-then statements.

Related StatementsThere are related conditionals that are based

on a given conditional statement. They are:

Converse

Inverse

Contrapositive

ConverseThe converse of a conditional statement is

formed by exchanging the hypothesis and the conclusion.

(Converse—con—switch)

Converse (Switch if-then)

Conditional:

If you live in Mishawaka, then you live in Indiana.

Converse:

If you live in Indiana, then you live in Mishawaka.

Inverse

The inverse of a conditional is formed by negating both the hypothesis and the conclusion.

(Negations state the opposite of the original phrase.)

Add not or take not out

not

Inverse (add not)

Conditional:

If you live in Mishawaka, then you live in Indiana.

Inverse:

If you don’t live in Mishawaka, then you don’t live in Indiana.

Contrapositive The contrapositive of a conditional is formed by

negating the hypothesis and conclusion, then interchanging them.

Switch and add not.

+not

Contrapositive(switch & add not)

Conditional:

If you live in Mishawaka, then you live in Indiana.

Contrapositive:

If you don’t live in Indiana, then you don’t live in Mishawaka.

If you are a teenager, then you are 15.

Converse:

If you are 15, then you are a teenager.

Inverse:

If you are not a teenager, then you are not 15.

Contrapositive:

If you are not 15, then you are not a teenager.

true

true

false

false

In your book on page 109

Statements with the same truth value are said to be logically equivalent.

A conditional and its contrapositive are either both true or both false. Similarly, the converse and inverse of a conditional are either both true or both false.

If you water the plants, then the plants will grow.

Converse:

If the plants grow, then you watered the plants.

Inverse:

If you don’t water the plants, then the plants will not grow.

Contrapositive:

If the plants do not grow, then you did not water the plants.

true

true

true

true

NATURE Write the converse, inverse, and contrapositive of the following true statement. Determine the truth value of each statement. If a statement is false, give a counterexample.

.

Bats are not birds, they are mammals.Bats have modified

hands and armsthat serve as wings.They are the only

mammals that can fly.

Conditional: First, rewrite the conditional in if-then form.

If an animal is a bat, then it can fly.

Bats are animals that can fly

Converse: If an animal can fly, then it is a bat.

Counterexample: A bird is an animal that can fly, but it is not a bat.

Inverse: If an animal is not a bat, then it cannot fly.

Counterexample: A bird is not a bat, but it is an animal that can fly.

Contrapositive: If an animal cannot fly, then it is not a bat.

T

F

F

T

Check Check to see that logically equivalent statements have the same truth value.

Both the conditional and contrapositive are true.

Both the converse and inverse are false.

2-3 Assignment day 2

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