Homework SourseProve that p rightarrow q leftrightarrow Tilde p vee q is a
Prove that (p rightarrow q) leftrightarrow (Tilde p vee q) is a tautology Using truth table Using logical equivalences/identities
Solution
a) A propositional expression is a tautology if and only if for all possible assignments of truth values to its variables its truth value is T.
Below is the truth table to prove that
P
Q
~P
~PVQ
P->Q
P->Q <-> ~PVQ
T
T
F
T
T
T
T
F
F
F
F
T
F
T
T
T
T
T
F
F
T
T
T
T
| P | Q | ~P | ~PVQ | P->Q | P->Q <-> ~PVQ |
| T | T | F | T | T | T |
| T | F | F | F | F | T |
| F | T | T | T | T | T |
| F | F | T | T | T | T |
