chapter 2 study sheet by Saray Sanchez

hypothesis

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if- then statement following 'if'

conclusion

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if-then statement following 'then'

coverse

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switching the hypothesis 7 conclusion of a conditional

inverse

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negating both the hypothesis and conclusion

contrapositive

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switching the hypothesis and conclusion & negating both

conjectures

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conclusion you reach using inductive reasoning

counterexamples

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an example that shows a conjecture is incorrect

addition property

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if a=b, then a+c=b

subtraction property

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if a=b, then a-c= b-c

multiplication property

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if a=b, then axc= bxc

division property

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if a=b & c does not =0, then a/c = b/c

reflexive property

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a=a

symmetric property

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if a=b , then b=a

transitive property

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if A=b, & b-=c then a=c

substitution property

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if a=b, then b can replace a in any expression

proofs

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involves writing reasoned,logical explanations that use definitions

law of syllogism

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allows you to state a conclusion for 2 true conditional statements

law of detachment

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if hypothesis of a true conditional is true, then conclusion is true

example one:

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write the conditional, converse, inverse, and contrapositive for the statement.
conditional: if minverse: if mcontrapositive: if

example 2:

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describe the property being used.
if B=A & A=C, then B=C

transitive prop.

example 3:

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describe the property being used
if OC = SS, then SS = OC

symmetric prop