Inductive Reasoning and Counterexample

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Inductive reasoning

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A conjecture is reached based on observations of a previous pattern.

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Counterexample

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An example that proves a conjecture is false.

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Negation of statement p

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not p

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Conjunction

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is formed by joining two or more statements with the word and

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DIsjunction

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a compound statement formed with the word or

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Conditional Statement

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an if-then statement written in the form if p, then q in which p is the hypothesis and q is the conclusion

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Law of Detachment

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If p→q is true and p is true, then q is also true

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Law of Syllogism

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If p→q and q→r are true, then p→r is also true

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Step 1 Proof

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List the given information and draw a diagram, if possible

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Step 2 Proof

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State what is to be proved