Section 2.2 Analyze Conditional Statements. Homework Pg 82 #3-5, 11-15, 19-21.

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Section 2.2 Analyze Conditional Statements

Homework Pg 82 #3-5, 11-15, 19-21

Vocabulary Conditional Statement-Logical agrument with two parts If-then form-hypothesis conclusion Negation-opposite of the original statement Equivalent statements-statements that hold the same truth value Perpendicular lines-two lines that intersect to form a right angle Biconditional Statements-conditional statements that contain the phrase “if and only if” Converse- exchange the hypothesis and conclusion of the original statement Inverse-negate both the hypothesis and conclusion Contrapositive- combination of converse and inverse

Rewrite a statement in if-then form Rewrite the conditional statement in if-then form. All birds have feathers. a. b. Two angles are supplementary if they are a linear pair. First, identify the hypothesis and the conclusion. When you rewrite the statement in if-then form, you may need to reword the hypothesis or conclusion. a. All birds have feathers. If an animal is a bird, then it has feathers.

Example Rewrite the conditional statement in if-then form. When n = 9, n 2 = 81. ANSWER If n = 9, then n 2 = 81. Tourists at the Alamo are in Texas. ANSWER If tourists are at the Alamo, then they are in Texas.

Write four related conditional statements Write the if-then form, the converse, the inverse, and the contrapositive of the conditional statement “Guitar players are musicians.” Decide whether each statement is true or false. If-then form: If you are a guitar player, then you are a musician. Converse: If you are a musician, then you are a guitar player. True, guitars players are musicians. False, not all musicians play the guitar.

Inverse: If you are not a guitar player, then you are not a musician. Contrapositive: If you are not a musician, then you are not a guitar player. False, even if you don’t play a guitar, you can still be a musician. True, a person who is not a musician cannot be a guitar player.

Write a biconditional Write the definition of perpendicular lines as a biconditional. Definition: If two lines intersect to form a right angle, then they are perpendicular. Converse: If two lines are perpendicular, then they intersect to form a right angle. Biconditional: Two lines are perpendicular if and only if they intersect to form a right angle.

Example Rewrite the statements as a biconditional. If Mary is in theater class, she will be in the fall play. If Mary is in the fall play, she must be taking theater class. Biconditional: Mary is in the theater class if and only if she will be in the fall play. ANSWER