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
Top Related