Question

Show that ¬(p ⊕ q) and p ↔ q are logically equivalent

Answer 1

Let us show that $¬(p ⊕ q)$ and $p ↔ q$ are logically equivalent using truth table:

$\begin{array}{||c|c||c|c|c|} \hline \hline p & q & p\oplus q & \neg(p\oplus q) & p ↔ q\\ \hline \hline F & F & F & T & T\\ \hline F & T & T & F & F\\ \hline T & F & T & F & F\\ \hline T & T & F & T & T\\ \hline \hline \end{array}$

Since the formulas on each pair have the same values, they are logically equivalent.