2.2 Conditional Statements Objective: Students will analyze statements in if-then form and write the converse, inverse, and contrapositive of if-then statements.

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2.2 Conditional Statements Objective: Students will analyze statements in if-then form and write the converse, inverse, and contrapositive of if-then statements.

Conditional Statements AA conditional statement is a statement that can be written in if-then form. AAn if-then statement is written in the form if p then q. The phrase immediately following the word if is the hypothesis. The phrase immediately following the word then is the conclusion.

Examples 1. Identify the hypothesis and conclusion: If a polygon has six sides, then it is a hexagon. 2. Write each statement in if-then form: 1. Distance is positive. 2. A five-sided polygon is a pentagon. 3. Determine the truth value of the following statement for each condition: If false, give a counterexample: 1. If a month has 28 days, then it is February 2. If two angles form a linear pair, then they are supplementary.

Related conditionals Other statements based on a given conditional statement.

Conditional  Formed by the given hypothesis and conclusion  p –> q “If a figure has three sides, then it is a triangle.”

Converse  Formed by exchanging the hypothesis and conclusion of the conditional.  q –> p “If a figure is a triangle, then it has three sides.”

Inverse  Formed by negating both the hypothesis and conclusion of the conditional.  ~p -> ~q “If a figure does not have three sides, then it is not a triangle.”

Contrapositive  Formed by exchanging AND negating the hypothesis and conclusion of the conditional.  ~q -> ~p “If a figure is not a triangle, then it does not have three sides.”

Example Write the converse, inverse, and contrapositive of the following statement. Then determine the truth value of each related conditional. “ If you live in Dallas, then you live in Texas.”