Question

The ‘Exclusive OR’ operation (also called XOR) between two propositions p and q is defined as follows:

p ⊕ q = (p ∨ q) ∧ ¬(p ∧ q)

Using laws of propositional logic prove the following:

(i.) Exclusive OR is commutative, i.e., p ⊕ q ≡ q ⊕ p.

(ii.) p ⊕ p is a contradiction.

(iii.) Conjunction distributes over Exclusive OR, i.e, for any proposition r,

r ∧ (p ⊕ q) ≡ (r ∧ p) ⊕ (r ∧ q).

Clearly state which law you are using in each step.

Answer 1