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+12 votes

Which of the following operations is commutative but not associative?

  1. AND
  2. OR
  3. NAND
  4. EXOR
in Digital Logic by Veteran | 3.8k views

2 Answers

+14 votes
Best answer
We all know AND ,OR are both associative and commutative.we dont know about EXOR and NAND

We can consume some time and prove it by truth table..and come up with the results that EXOR is also associative and commutative so the only left out is NAND  its commutative but not associative

Correct Answer: $C$
by Boss
edited by
Its good to remember-
1)Every logic gate follows Commutative law.
2)AND,OR,Ex-OR,EX-NOR follows Associative law. NAND,NOR doesn`t follow Associative law.
NOT also doesnt follow associative law

am i right ??
NOT is not even a Binary operator, its unary operator.
yes .. thanks

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tell me where i can study these topic
implication is not commutative is it true?
Adding one more point,


AND, OR follows even distributive law also.

+2 votes
Ans: C NAND and NOR does not follow associative rule
by Loyal
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