Ex. 1 Identifying Hypothesis and Conclusion A conditional is an If, then statement Made of two parts Hypothesis and conclusion Hypothesis follows the.

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Presentation transcript:

Ex. 1 Identifying Hypothesis and Conclusion A conditional is an If, then statement Made of two parts Hypothesis and conclusion Hypothesis follows the if Conclusion follows the then Identify hypothesis and conclusion of statements If today is the first day of fall, then the month is September. Hyp – first day of fall Conc – month is september If y - 3 = 5, then y = 8. Hyp – y – 3 = 5 Conc – y = 8

Ex. 2 Writing a Conditional Write each sentence as a conditional. Identify hyp and conclusion A rectangle has four right angles. If a figure is a rectangle, then it has four right angles. A tiger is an animal. If something is a tiger, then it is an animal. An integer that ends in 0 is divisible by 5. If an integer ends in 0, then it is divisible by 5. A square has four congruent sides. If a figure is a square, then it has four congruent sides.

Ex. 3 Finding a Counterexample Conditionals have truth value How true or false True – show everytime hyp is true, the conclusion must also be true False – needs a counterexample Counterexample proves something wrong Tell if T or F, if F give counterexample If it is February, then there are only 28 days in the month. F – leap year If x 2 ≥ 0, then x ≥ 0. F – x = -1

Ex. 5 Writing Converses Converse – switch hyp and conc of if, then statement Write converse Conditional If two lines intersect to form right angles, then they are perpendicular. Converse If two lines are perpendicular, then they intersect to form right angles. Conditional If two lines are not parallel and do not intersect, then they are skew. Converse If two lines are skew, then they are not parallel and do not intersect.

Ex. 6 Finding Truth Value of a Converse Write the converse and see if can find a counterexample If a figure is a square, then it has four sides. If a figure has four sides, then it is a square. F - Counter is rectangle If two lines do not intersect, then they are parallel. If two lines are parallel, then they do not intersect. True

Symbolic Form P = hypothesis Q = conclusion Conditional p → q reads as If p, then q Converse q → p reads as If q, then p