ITPEC FE Morning October 2018 Question 1
Which of the following is a logical expression equivalent to the exclusive-OR operation of logical variables p and q? Here, “∨”, “∧”, and “¬” are OR, AND, and NOT operators, respectively.
Explanation
(p ∨ q) ∧ ¬(p ∧ q) — exclusive OR is true when exactly one input is true: at least one is true, and not both.
The last two columns agree on every row, so the expression is equivalent to XOR.
Answer (b)
Why not others:
- •(a) — ¬p ∨ q is implication, p → q; it is 1 when p = q = 0 and when both are 1, where XOR is 0
- •(c) — ¬(p ∨ q) ∨ (p ∧ q) is 1 exactly when p and q are equal: the negation of XOR (XNOR)
- •(d) — p ∧ ¬q is already contained in ¬(q ∧ p), so the whole expression reduces to NAND, which is 1 at p = q = 0
Key rule: Check a logical equivalence with a four-row truth table, and remember XOR as "OR but not AND": (p ∨ q) ∧ ¬(p ∧ q), or (p ∧ ¬q) ∨ (¬p ∧ q).
Basic Theory · AI-written, may contain errors
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