Two logical statements p and q are said to be logical equivalents. It is denoted by p≡q when if p⇔q is a tautology.
Note: Do not write p = q; instead write p ≡ q.
Note: It doesn’t mean that p and q are equal. Since p and q are different statements, they cannot be the same. Logical Equivalence means, that p and q always produce the same truth values. This is why we write p≡q, not p=q.
Example: p⇒q≡~p∨q
| p | q | ~p | p⇒q | ~pVq |
| T | T | F | T | T |
| T | F | F | F | F |
| F | T | T | T | T |
| F | F | T | T | T |
So here p⇒q and ~p∨q both are producing the same truth values. That means they are equivalent (p⇒q≡~p∨q).
