The compound proposition that has the same truth values in all possible
cases is called logical equivalence. OR The proposition p and q is logical
equivalent if p↔q is a tautology.
Eg: ~(p ˄ q) and ~p ∨ ~q are
logically equivalent.
|
p
|
q
|
¬p
|
¬q
|
p ˄ q
|
¬ (p ˄ q)
|
¬p ∨ ¬q
|
¬ (p ˄ q) ↔ ¬p ∨ ¬q
|
|
T
|
T
|
F
|
F
|
T
|
F
|
F
|
T
|
|
T
|
F
|
F
|
T
|
F
|
T
|
T
|
T
|
|
F
|
T
|
T
|
F
|
F
|
T
|
T
|
T
|
|
F
|
F
|
T
|
T
|
F
|
T
|
T
|
T
|
Since, ¬ (p ˄ q) ↔ ¬p ∨ ¬q is a tautology we can say that ¬ (p ˄ q) and ¬p
∨ ¬q are logically equivalent.
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