2 4 ways to write statements: Conditional statementConverseInverseContrapositive
3 Conditional Statements A _________________ is a statement that can be expressed in ________form.“if-then”2. A conditional statement has _________.The __________ is the ____ part.The __________ is the ______ part.two partshypothesis“if”conclusion“then”
4 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: conclusionSometimes written as: p q
5 Example : Writing a Conditional Statement Write a conditional statement from the following.“An obtuse triangle has exactly one obtuse angle.”An obtuse trianglehas exactly one obtuse angle.Identify the hypothesis and the conclusion.If a triangle is obtuse, then it has exactly one obtuse angle.
6 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 pA statement and its converse say different things. Some true statements have FALSE converses.
7 Inverse and Contrapositive Negation: uses this symbol: ~~p is read not pStatement: p q3) Inverse: ~p ~q4) Contrapositive: ~q ~pOn 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: ~ ___ ~ ____
8 Recap: Conditional Statements ( )Converse( )Inverse( ~p ~q )Contrapositive( ~q ~p )If I am sleeping, then I am breathing.p qIf I am breathing, then I am sleeping.q pIf I am not sleeping, then I am not breathing.If I am not breathing, then I am not sleeping.
9 Ex. Conditional Statements If m<A = 30°, then <A is acute.Inverse(insert not)Converse(switch)Contrapositive(switch then insert not)TIf m<A ≠ 30°, then <A is not acute.FIf <A is acute, thenm<A = 30°.FIf <A is not acute, then m<A ≠ 30°.T
10 Ex. Identify the underlined portion of the conditional statement. hypothesisConclusionneither
11 Ex. Identify the underlined portion of the conditional statement. hypothesisConclusionneither
12 Ex. Identify the converse for the given conditional. If you do not like tennis, then you do not play on the tennis team.If you play on the tennis team, then you like tennis.If you do not play on the tennis team, then you do not like tennis.You play tennis only if you like tennis.
13 Identify the inverse for the given conditional. If 2x is not even, then x is not odd.If 2x is even, then x is odd.If x is even, then 2x is odd.If x is not odd, then 2x is not even.