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Download 2-2 = Conditional Statements
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Conditional Statements Conditional Statement True under certain conditions Can be written in the form If _____, then _____. Hypothesis the “if” part what has to happen first antecedent or prerequisite Conclusion the “then” part what will happen after the hypothesis occurs consequent Identify the hypothesis and conclusion in these statements. We have shorter classes at Garrigan when there’s mass. We have shorter classes at Garrigan when there’s mass. H = there’s mass C = shorter classes at Garrigan Since it was raining, she took an umbrella with her. Since it was raining, she took an umbrella with her. H = it was raining C = she took an umbrella with her. We had a substitute because the teacher was sick. We had a substitute because the teacher was sick. H = the teacher was sick C = we has a substitute If you get a BB gun, you’ll shoot your eye out. If you get a BB gun, you’ll shoot your eye out. H = you get a BB gun C = you’ll shoot your eye out Being enrolled in Geometry implies having passed Algebra I. (This one is a trick question.) Being enrolled in Geometry implies having passed Algebra I. H = Being enrolled in Geometry C = Passed Algebra I Standard Notation for if/then AB This means “If A, then B” or “A implies B” Write this sentence in if/then form: Parallel lines have the same slope. Write this sentence in if/then form: Parallel lines have the same slope. If lines are parallel, then they have the same slope. In Geometry we care about the truth value of statements In order for a conditional statement to be true … every time the hypothesis is true, the conclusion must also be true So … “If there’s a teacher inservice, then we get out early” is true. “If we get out early, then there’s a teacher inservice” is false. Alternative conditional statements … Converse The converse of A B is B A Switch around the hypothesis and conclusion. Find the converse of … If today is Thursday, then tomorrow is Friday. If 2 angles of a triangle have the same measure, then 2 sides of the triangle have the same measure. Find the converse of … If there’s mass, then classes are short. All squares are rectangles. The last two examples show that the converse is not necessarily true. In logic, the symbol ~ means NOT. Inverse The inverse of A B is ~A ~B Make both parts negative. (Keep order the same.) Find the inverse of … If today is Thursday, then tomorrow is Friday. If 2 angles of a triangle have the same measure, then 2 sides of the triangle have the same measure. Find the inverse of … If there’s mass, then classes are short. All squares are rectangles. The last two examples show that the inverse is not necessarily true. Contrapositive The converse of A B is ~B ~A Backwards AND negative Converse of the inverse Find the contrapositive of … If today is Thursday, then tomorrow is Friday. If 2 angles of a triangle have the same measure, then 2 sides of the triangle have the same measure. Find the contrapositive of … If there’s mass, then classes are short. All squares are rectangles. If a conditional is true, then its contrapositive is also true. A statement and its contrapositive are logically equivalent. A B ~B ~A REMEMBER conditional hypothesis conclusion converse inverse contrapositive logically equivalent
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