GATE CS Mastery
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GATE CS 2015 Set 1 · Digital Logic

Question 38

MCQPrinted as CS Q.282 marksWrong answer: −2/3Easy (estimate)

Question

The binary operator ≠\ne is defined by the following truth table:

pp qq p≠qp \ne q
0 0 0
0 1 1
1 0 1
1 1 0

Which one of the following is true about the binary operator ≠\ne?

Choose one option
Official answer and solution
Official answer
A
From
Official GATE 2015 answer key

Solution

Identify the binary truth table as the exclusive-OR (XOR) operator and verify its algebraic properties.

From the given truth table:

  • 0≠0=00 \ne 0 = 0
  • 0≠1=10 \ne 1 = 1
  • 1≠0=11 \ne 0 = 1
  • 1≠1=01 \ne 1 = 0

This is the truth table of the Exclusive-OR (XOR, ⊕\oplus) operation.

Properties of XOR:

  1. Commutativity: p⊕q=q⊕pp \oplus q = q \oplus p holds for all Boolean values.
  2. Associativity: (p⊕q)⊕r=p⊕(q⊕r)(p \oplus q) \oplus r = p \oplus (q \oplus r) holds because XOR corresponds to addition modulo 2, which is associative.

Therefore, the operator ≠\ne is both commutative and associative (option A).

Final answer

A

Common trap

Confusing XOR with implication or NAND, which are not associative.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2015 Computer Science and Information Technology (CS) Session 1
Question
38 of 65, printed as CS Q.28
Section
Computer Science and Information Technology

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