2.2: If-Then Statements

p. 76-83

• 4 ways to write statements:

1. Conditional statement

2. Converse

3. Inverse

4. Contrapositive

Conditional StatementsConditional Statements

1.1. A _________________ is a statement A _________________ is a statement that can be expressed in that can be expressed in ________________form.form.

conditional statementconditional statement““if-then”if-then”

2.2. A conditional statement has A conditional statement has __________________..The The ____________________ is the is the ________ part. part.The The ____________________ is the is the ____________ part. part.

hypothesishypothesistwo partstwo parts

““if”if”conclusionconclusion ““then”then”

1)If then statements (also called conditionals, or statements)

“If it rains after school, then I will give you a ride home.”

If p, then q.

p: hypothesis q: conclusion

Sometimes written as: p q

Write a conditional statement from the following.

Example : Writing a Conditional Statement

“An obtuse triangle has exactly one obtuse angle.”

If a triangle is obtuse, then it has exactly one obtuse angle.

Identify the hypothesis and the conclusion.

An obtuse triangle

has exactly one obtuse angle.

2) Converse of a conditionals

(q p) Converse – the converse of a conditional is formed by switching the hypothesis and conclusion.

Conditional:“If Ed lives in Texas, then he lives south of Canada.” p qConverse“If Ed lives south of Canada, then he lives in Texas.” q p

A statement and its converse say different things. Some true statements have FALSE converses.

• Negation: uses this symbol: ~ • ~p is read not p• Statement: p q• 3) Inverse: ~p ~q• 4) Contrapositive: ~q ~p

– On Your Own: • For the statement below, first define the hypothesis and conclusion in

symbols then write the converse, inverse and contrapositive in symbols.• Statement: If the sky is clear tomorrow morning, then I’ll go for a run.• r: ___________________________• s: ___________________________• Statement : ___ ___, • Converse: ___ ___• Inverse: ~ ___ ~ ___• Contrapositive: ~ ___ ~ ____

Inverse and Contrapositive

Recap: Conditional StatementsRecap: Conditional StatementsConditionalConditional

( )( )

ConverseConverse

( )( )

InverseInverse

( ( ~p~p ~q~q ) )

ContrapositiveContrapositive

( ( ~q~q ~p~p ) )

If If I amI am sleepingsleeping, then , then I amI am breathingbreathing..

If If I amI am breathingbreathing, then , then I amI am sleepingsleeping..

If If I am notI am not sleepingsleeping, then , then I am I am notnot breathingbreathing..

If If I am I am notnot breathingbreathing, then , then I I am am notnot sleeping sleeping..

pp qq

qq pp

Ex. Conditional StatementsEx. Conditional StatementsConditionalConditional If If mm<A = 30<A = 30°°, then <A is , then <A is

acute.acute.

InverseInverse

(insert not)(insert not)

ConverseConverse

(switch)(switch)

ContrapositiveContrapositive

(switch then (switch then insert not)insert not)

TT

TT

FF

FF

If If mm<A <A ≠≠ 30°, then <A is 30°, then <A is not not acute.acute.

If <A is acute, then If <A is acute, then

mm<A = 30°.<A = 30°.

If <A is If <A is not not acute, then acute, then mm<A <A ≠≠ 30°. 30°.

Ex. Identify the underlined portion Ex. Identify the underlined portion of the conditional statement.of the conditional statement.

A.A. hypothesishypothesis

B.B. ConclusionConclusion

C.C. neitherneither

Ex. Identify the underlined portion Ex. Identify the underlined portion of the conditional statement.of the conditional statement.

A.A. hypothesishypothesis

B.B. ConclusionConclusion

C.C. neitherneither

Ex. Identify the converse for Ex. Identify the converse for the given conditional.the given conditional.

A.A. If you do not like tennis, then you do not If you do not like tennis, then you do not play on the tennis team.play on the tennis team.

B.B. If you play on the tennis team, then you If you play on the tennis team, then you like tennis.like tennis.

C.C. If you do not play on the tennis team, then If you do not play on the tennis team, then you do not like tennis.you do not like tennis.

D.D. You play tennis only if you like tennis.You play tennis only if you like tennis.

Identify the inverse for the given Identify the inverse for the given conditional.conditional.

A.A. If 2x is not even, then x is not odd.If 2x is not even, then x is not odd.

B.B. If 2x is even, then x is odd.If 2x is even, then x is odd.

C.C. If x is even, then 2x is odd.If x is even, then 2x is odd.

D.D. If x is not odd, then 2x is not even.If x is not odd, then 2x is not even.

Assignment

• P. 80 (6-17, 22, 23, 27, 29, 30, 36, 39)