Exclusive Or Symbolisation – UGC NET Question

The phrase “either P or Q, but not both” specifies exclusive disjunction. This means at least one of P or Q is true, and they are not simultaneously true. Symbolically, we combine the inclusive disjunction P ∨ Q with the negation of their conjunction, ¬(P ∧ Q). The conjunction of these two conditions, (P ∨ Q) ∧ ¬(P ∧ Q), precisely encodes exclusivity.

Option A:
Option A, P ∨ Q, is inclusive “or” and allows the possibility that both P and Q are true, which is not allowed in the exclusive reading.

Option B:
Option B adds the restriction that P and Q cannot both hold, yielding the desired “one but not both” condition.

Option C:
Option C, P ∧ Q, demands that both P and Q are true together, the opposite of what exclusivity requires.

Option D:
Option D expresses logical equivalence or biconditional, requiring P and Q to share the same truth value, which is different from exclusive disjunction.