Conditional Statement Geometry Ms. Olifer

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Presentation transcript:

Conditional Statement Geometry Ms. Olifer

Conditional Statements Conditional Statement – if/then form; has a hypothesis and a conclusion Inverse Converse Contrapositive negation of the hypothesis and conclusion switch the conclusion and the hypothesis negate the converse

The Parts of Conditional In an if-then statement, the clause following the “if” is called the hypothesis. The clause following the “then” is the conclusion. Ex. If a figure is a segment, then it’s a convex set. hypothesis conclusion

If it is Saturday, then we will shop. Hypothesis: Conclusion: Inverse: Converse: Contrapositive: It is Saturday We will shop If it isn’t Saturday then we will not shop. If we shop then it is Saturday. If we don’t shop, then it isn’t Saturday.

If you see lightening, then you hear thunder. Hypothesis: Conclusion: Inverse: Converse: Contrapositive: You see lightening You hear thunder If you don’t see lightening then you don’t hear thunder. If you hear thunder then you see lightening. If you don’t hear thunder then you won’t see lightening.

Definition An instance of a conditional is a specific case in which both the antecedent (if part) and the consequent (then part) of the conditional are true. A counterexample to a conditional is a specific case for which the antecedent (if part) of the conditional is true and its consequent (then part) is false.

Important! If a given conditional statement is true, the converse and inverse are not necessarily true. However, the contrapositive of a true conditional statement is always true, and the contrapositive of a false conditional is always false.

If Johnny Depp will star in Pirates of the Caribbean IV, The Search for More Dough, then he won’t have to worry about money. Johnny Depp will star in Pirates of the Caribbean IV – The Search for More Dough Hypothesis: Conclusion: Inverse: He won’t have to worry about money. If Johnny Depp does not star in Pirates of the Caribbean IV, then he will have to worry about money.

If Johnny Depp will star in Pirates of the Caribbean IV, The Search for More Dough, then he won’t have to worry about money. Converse: Contrapositive: If he doesn’t have to worry about money then Johnny Depp will star in Pirates of the Caribbean IV. If he has to worry about money then Johnny Depp will not star in in Pirates of the Caribbean IV.