Chapter 2: Connecting Reasoning and Proof Study Sheet by Diana Gatica

Conclusion

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Is the part of an if-then statement(conditional) that follows then.

Hypothesis

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In an if-then statement (conditional) the hypothesis is the part that follows if.

Converse

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The statement obtained by reversing the hypothesis and conclusion of a conditional.

Inverse

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The inverse of the conditional "if p, then q" is the conditional "if not p, then not q."

Contrapositive

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The contrapositive of the conditional "if p. then q" is the conditional "if not q, then not p."

If-then Form

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If p, then q and if q, then p.
Or p<-->q.

Conjecture

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Is a conclusion reached by using inductive reasoning.

Counterexample

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example showing that a statement is false.

All Properties

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Addition Prop - If a=b, then a+c=b+c.
Subtraction Prop - If a=b, then a-c=b-c.
Mult. Prop - If a=b, then axc=bxc.
Division Prop - If a=b and c doesn't = 0, the a/c=b/c.
Reflexive Prop - a=a.
Symmetric Prop - If a=b, then b=a.
Transitive Prop - If a=b and b=c, then a=c.
Substitution Prop - If a=b, then b can be replace a in any expression.

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Law of Detachment

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If the hypothesis of a true conditional is true, then the conclusion is true.

Law of Syllogism

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Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement.

Example#1: If a=b+2, and b+2=c, then a=c.

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Answer: Transitive

Example #2: If a student gets an A on a final exam, then the student will pass the course. Felicia got an A on her history final exam.

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If a student gets an A on a final exam (P), then the student will pass the course (Q). Felicia got an A on her history final exam (P). Answer: Felicia will pass her history course.

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Example#3: If
Answer: