chapter two by Jenna Wycoff

Inductive Reasoning

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You use inductive reasoning when you make observations based on patterns that you observe.

Conjecture

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A conjecture is a conclusion you reach using inductive reasoning

Counter Example

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A counter Example is an example that shows a conjecture is incorrect.

2-1 Example

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1, -3, 9, -27....
Each term is (-3) multiplied to the previous number. The next two terms would be -27 * (-3) = 81 and 81 * (-3) + -243

Conditional

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A conditional is an if, then statement. The symbolic form of a conditional is p ---> q, where p is the hypothesis and q is the conclusion.

Converse

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To fine the converse, switch the hypothesis and conclusion for the conditional.

Inverse

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You negate the hypothesis and conclusion of the conditional.
EX: ( ~p ---> ~q )

Contrapositive

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negate the hypothesis and the conclusion of the converse.
EX: (~q ---> ~p)

2-2 Example

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Biconditionals

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When conditionals and their converses are true, you can combine them as a true biconditional using the phrase "if and only if". The symbolic term is p <--> q.

Deductive Reasoning

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The process of reasoning logically from given statements to a conclusion

Law of Detachment

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If p --> q is true and p is true, then q is true

Law of Syllogism

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If p --> q and q ---> r are true, then p --> r is true.

Law of Syllogism Example

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Proof

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A proof is a convincing argument that uses deductive reasoning.

Two column proof

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Lists each statement on the left, and the reasons why on the right.

Theorum

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A statement that you prove true.

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In geometry, each statement in a proof is justified by given info, a property, postulate, definition, or theorem