2ExampleYou cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.
3Basic Terminology A tautology is a proposition which is always true. p pA contradiction is a proposition that is always false.p pA contingency is a proposition that is neither a tautology nor a contradiction.p q r
4Logical EquivalencesTwo propositions p and q are logically equivalent if they have the same truth values in all possible cases.Two propositions p and q are logically equivalent if p q is a tautology.Notation: p q or p q
5Determining Logical Equivalence Use a truth table.Show that (p q) and p q are logically equivalent.Not a very efficient method, WHY?Solution: Develop a series of equivalences.
6Important Equivalences Identityp T pp F pDominationp T Tp F FIdempotentp p pp p pDouble Negation( p) p