More Conditional Statements

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Presentation transcript:

More Conditional Statements Lesson 17 More Conditional Statements

Review of Conditional Statements A conditional statement is a statement in the form “If p, then q.” p is the hypothesis q is the conclusion The converse of a statement is formed by exchanging the hypothesis and conclusion “If q, then p.” A counterexample is an example that proves a conjecture or statement is false

If tomorrow is Wednesday, then yesterday was Monday. State hypothesis and conclusion Write the converse Find the truth value of original and converse. If false, then give a counterexample. Hypothesis – tomorrow is Wednesday Conclusion – yesterday was Monday If yesterday was Monday, then tomorrow is Wednesday. Both are true

Conditional Statements New Vocabulary The negation of a statement is the opposite of that statement not p can be written as ~p “the sky is blue” negation is “the sky is not blue” When 2 statements have the same truth value, they are logically equivalent statements The inverse of a statement negates the hypothesis and conclusion The contrapositive of a statement exchanges and negates hypothesis and conclusion Conditional Statements Form Original If p, then q. Converse If q, then p. Inverse If ~p, then ~q. Contrapositive If ~q, then ~p.

If a number is not divisible by 2, then the number is odd. Write the inverse of the statement Is the statement true? Is the inverse true? If a number is divisible by 2, then the number is not odd. Original is true Inverse is true

If two angles form a linear pair, then they are supplementary. Write the contrapositive Determine the truth value of both original and contrapositive If two angles are not supplementary, then they do not form a linear pair. Both are true This is not a coincidence The original and contrapositive are logically equivalent statements Future lessons we will use the contrapositive to prove/disprove statements

Questions/Review You will be asked to write many statements throughout this assignment Some will have you write all four while others may not You should also label each statement because they are not always asked in the same order This lesson will be reference in lesson 20 and will be helpful in determining truth values in the future