Which of the following operation is commutative but not associative
1998
Which of the following operation is commutative but not associative
- A.
AND
- B.
OR
- C.
NAND
- D.
EXOR
Attempted by 112 students.
Show answer & explanation
Correct answer: C
To determine which gate is commutative but not associative, let's test the laws using the NAND operation (↑):
Commutative Law (A ↑ B = B ↑ A):
~(A . B) = ~(B . A)
Since standard multiplication (AND) is commutative, NAND is also commutative.'
2. Associative Law ((A ↑ B) ↑ C = A ↑ (B ↑ C)):
Left-Hand Side (LHS):
(A ↑ B) ↑ C = ~(A . B) ↑ C = ~(~( A . B) . C) = ~~(A . B) + ~C = (A . B) + ~C
Right-Hand Side (RHS):
A ↑ (B ↑ C) = A ↑ ~(B . C) = ~A . ~(B . C) = ~A + ~(B . C) = ~A + ~(B . C)
Since (A . B) + ~C ≠ ~ A + (B . C), the operation is not associative.