IPA FE Subject A 2024 Question 1

X □ Y is 0 only for X = 1, Y = 0 — read each half of the given table where it pins down X □ Y: the AND column where X = 1, the OR column where X = 0.

• •X = 1: with Z = X □ Y, 1 AND Z equals Z, so the AND column gives X □ Y directly: 1 □ 0 = 0 and 1 □ 1 = 1
• •X = 0: 0 OR Z equals Z, so the OR column gives X □ Y directly: 0 □ 0 = 1 and 0 □ 1 = 1
• •The remaining rows say nothing: with X = 0 the AND is always 0, and with X = 1 the OR is always 1

So X □ Y is 1, 1, 0, 1 for the inputs 00, 01, 10, 11. This is (NOT X) OR Y, the implication “if X then Y”.

Answer (c)

Why not others:

• •(a) — this is X AND Y: it gives 0 for 0 □ 0, so X OR (X □ Y) would be 0 in the first row, not 1
• •(b) — this is just Y: it gives 0 for 0 □ 0, which again makes the first row’s OR 0
• •(d) — this is NAND: it gives 0 for 1 □ 1, so X AND (X □ Y) would be 0 in the last row, not 1

Key rule: 1 AND Z = Z and 0 OR Z = Z, while 0 AND Z = 0 and 1 OR Z = 1 hide Z; use the rows where the known operand passes the unknown one through.

Basic Theory · AI-written, may contain errors