Consider the following statements regarding Logic Gates:1.NAND and NOR gates are universal gates capable of implementing any Boolean function.2.XOR gate follows associative law under all conditions of logic operations.3.AND gate operation is commutative and associative in Boolean algebra.Which of the above statements is/are correct?

Correct Answer: D - 1, 2 and 3

Quick Concept Explanation

Boolean algebra has operation-specific laws. AND and OR satisfy commutative and associative laws; XOR also satisfies commutative and associative laws, although it is not idempotent (A⊕A=0). Key relation: NAND universality: NOT A=A NAND A; AND from double NAND; OR via De Morgan. XOR associativity: A⊕B⊕C is independent of grouping.

Exam focus: Do not confuse XOR’s non-idempotent property with associativity. Common trap: Assuming XOR is non-associative because its output changes with parity.

Statement-wise Verification

• Statement 1 - Correct.
  NAND and NOR gates are universal gates capable of implementing any Boolean function.
  Any Boolean function can be constructed using NAND alone or NOR alone.
• Statement 2 - Correct.
  XOR gate follows associative law under all conditions of logic operations.
  XOR is associative, so A⊕(B⊕C)=(A⊕B)⊕C for binary Boolean operands.
• Statement 3 - Correct.
  AND gate operation is commutative and associative in Boolean algebra.
  Boolean algebra has operation-specific laws.

Core Concept

Boolean algebra has operation-specific laws. AND and OR satisfy commutative and associative laws; XOR also satisfies commutative and associative laws, although it is not idempotent (A⊕A=0). Universal-gate status means functional completeness, not that every gate has the same truth table.

Formula / Key Relationship

NAND universality: NOT A=A NAND A; AND from double NAND; OR via De Morgan. XOR associativity: A⊕B⊕C is independent of grouping.

Step-by-Step Check

Truth-table or algebraic verification confirms each statement. Therefore D (1,2,3) is the complete answer.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 2. Option C is incorrect because it omits correct statement(s) 1.

Answer-Key Verification Note

The uploaded provisional key marks B . After independent technical verification, the defensible answer is D . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

Do not confuse XOR’s non-idempotent property with associativity.

Common Mistake

Assuming XOR is non-associative because its output changes with parity.

Quick Revision

Universal Gates and Algebraic Properties is linked with Boolean Operators, Logic Gates and Digital Electronics. Do not confuse XOR’s non-idempotent property with associativity.