Conditional Statements

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Presentation transcript:

Conditional Statements Definition: A statement written in two parts, a hypothesis and a conclusion. When the conditional sis written in if-then form, the “if” part is the hypothesis and the “then” part is the conclusion. Example: If today is Monday, then tomorrow is Tuesday. “today is Monday” is the hypothesis “tomorrow is Tuesday” is the conclusion

Converse Definition: Formed by exchanging the hypothesis and conclusion. Original: If today is Monday, then tomorrow is Tuesday. Converse: If tomorrow is Tuesday, then today is Monday.

Inverse Definition: Make both the conclusion and hypothesis negative. Original: If today is Monday, then tomorrow is Tuesday. Inverse: If today is NOT Monday, then tomorrow is NOT Tuesday.

Contrapositive Definition: The converse of the inverse. (Flip the hypothesis and conclusion and make both negative) Original: If today is Monday, then tomorrow is Tuesday. Contrapostive: If tomorrow is NOT Tuesday, then today is NOT Monday.

Format Conditional Statement A  B Converse B  A Inverse NOT A  NOT B Contrapositive NOT B  NOT A

Counterexample Definition: Proof that a conditional statement could be in incorrect, in at least one instance. Example: If Sam lives in Florida, then he must live in Orlando. Counterexample: Sam could live in Miami.

Inductive Reasoning Definition: the process of observing data, recognizing patterns, and making generalizations about those patterns.

Conjecture Definition: the conclusion or generalization developed while using inductive reasoning.

Practice Your Inductive Reasoning Skills… Find the next three terms in the sequence. 2, 4, 7, ___, ___, ___ 1, 1, 2, 3, 5, 8, ____, ____, ____ 8, 11, 15, 20, ____, _____, _____ 5, 25, 125, ____, _____, _____