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2.2: If-Then Statements p

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**4 ways to write statements:**

Conditional statement Converse Inverse Contrapositive

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**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 parts hypothesis “if” conclusion “then”

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**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

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**Example : Writing a Conditional Statement**

Write a conditional statement from the following. “An obtuse triangle has exactly one obtuse angle.” An obtuse triangle has exactly one obtuse angle. Identify the hypothesis and the conclusion. If a triangle is obtuse, then it has exactly one obtuse angle.

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**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 q Converse “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.

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**Inverse and Contrapositive**

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: ~ ___ ~ ____

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**Recap: Conditional Statements**

( ) Converse ( ) Inverse ( ~p ~q ) Contrapositive ( ~q ~p ) If I am sleeping, then I am breathing. p q If I am breathing, then I am sleeping. q p If I am not sleeping, then I am not breathing. If I am not breathing, then I am not sleeping.

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**Ex. Conditional Statements**

If m<A = 30°, then <A is acute. Inverse (insert not) Converse (switch) Contrapositive (switch then insert not) T If m<A ≠ 30°, then <A is not acute. F If <A is acute, then m<A = 30°. F If <A is not acute, then m<A ≠ 30°. T

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

hypothesis Conclusion neither

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

hypothesis Conclusion neither

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**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.

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**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.

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

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