1.3 Equivalence
Logical equivalence compares formulas by their truth values under all valuations, rather than by their written form, and it gives a precise way to say that two formulas express the same logical content. Definition 1.17 (Logical Equivalence) Let $A$ and $B$ be formulas. We say that $A$ and $B$ are logically equivalent if: $$ v(A)=v(B) $$ for every valuation $v$. In this case we write: $$ A \equiv B $$...