Conditional StatementA conditional statement has two parts, a hypothesis and a conclusion.

When conditional statements are written in if-then form, the part after the “if” is the hypothesis, and the part after the “then” is the conclusion.

p → q

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Example 1: State the hypothesis and conclusion.If you are 13 years old, then you are a

teenager.Hypothesis:

You are 13 years oldConclusion:

You are a teenager

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Example 1: Rewrite in the if-then formAll mammals breathe oxygen

If an animal is a mammal, then it breathes oxygen.

A number divisible by 9 is also divisible by 3If a number is divisible by 9, then it is

divisible by 3.

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NegationThe negative of the statementExample: Write the negative of the statement

A is acuteA is not acute

~p represents “not p” or the negation of p

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Converse, Inverse and Contrapositive

ConverseThe converse of a conditional is formed by

switching the hypothesis and the conclusion.The converse of p → q is q → p

InverseNegate the hypothesis and the conclusionThe inverse of p → q, is ~p → ~q

ContrapositiveNegate the hypothesis and the conclusion of the

converseThe contrapositive of p → q, is ~q → ~p.

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ExampleWrite the (a) inverse, (b) converse, and (c)

contrapositive of the statement.If two angles are vertical, then the angles are

congruent.(a) Inverse: If 2 angles are not vertical, then

they are not congruent.(b) Converse: If 2 angles are congruent, then

they are vertical.(c) Contrapositive: If 2 angles are not

congruent, then they are not vertical.

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Equivalent StatementsWhen 2 statements are both true or both falseA conditional statement is equivalent to its

contrapositive.The inverse and the converse of any conditional are

equivalent.

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Biconditional Statementp if and only if qp iff. q

Biconditional StatementIt is Saturday, if and only if I am working at the

restaurant.

Conditional StatementIf it is Saturday, then I am working at the

restaurant.

Rewrite the biconditional as conditional statement and its converse.Two angles are supplementary if and only if

the sum of their measures is 180°.

Conditional:If two angles are supplementary, then the sum

of their measures is 180°.

Converse:If the sum of two angles measure 180°, then

they are supplementary.

Conditional Statement:If it rains, then the game will be cancelled.

Write down one of the following. Move to the correct corner: inverse, converse, or contrapositive.

If the game is cancelled, then it has rained.

If it does not rain, then the game will not be cancelled.

If the game is not cancelled, then it has not rained.

Converse

Inverse

Contrapositive

Conditional Statement:If there is snow on the ground, then flowers are not in bloom.

Write down one of the following. Move to the correct corner: inverse, converse, or contrapositive.

If there is no snow on the ground, then flowers are in bloom.

If flowers are not in bloom, then there is snow on the ground.

If flowers are in bloom, then there is no snow on the ground.Converse

Inverse

Contrapositive

Conditional Statement:If two points are collinear, then they lie on the same line.

Write down one of the following. Move to the correct corner: inverse, converse, or contrapositive.

If two points lie on the same line, then they are collinear.

If two points do not lie on the same line, then they are not collinear.

If two points are not collinear, then they do not lie on the same line.

Contrapositive

Converse

Inverse