Inverse, Contrapositive & indirect proofsSections 6.2/6.3

Converse• Switches hypotheses and

conclusion.Statement: if this is silly then it is

useless.Converse: if this is useless then it

is silly.

Inverse• Negates hypotheses and

conclusion.Statement: if this is silly then it is

useless.Converse: if this is not silly then it

is not useless.

Contrapositive• Negates and switches

hypotheses and conclusion.Statement: if this is silly then it is

useless.Converse: if this is not useless

then it is not silly.

Logically equivalent• Two statements that are always both

true or both false.• A Statement and the contrapositive

are logically equivalent.• The inverse and converse of a

statement are logically equivalent

Indirect Proofs

• Assume temporarily that conclusion is not true.• Reason logically until you

reach a contradiction of a known fact