UGC NET CSE | December 2012 | Part 2 | Question: 49

Question

Identify the operation which is commutative but not associative?

• A. OR
• B. NOR
• C. EX-OR
• D. NAND

Answer 1

B and D are answers

A. OR:

0+1 = 1+0  =1  => Commutative

(0+1)+1= 1+1 =1                            0+(1+1)= 0+1 =1 => Associative

B. NOR

0 NOR 1 = 1 NOR 0 =0 => Commutative

(0 NOR 1) NOR 1 =0 NOR 1 = 0             0 NOR(1 NOR 1) =0 NOR 0 = 1 => Not associative

C. XOR

0 XOR 1 = 1 XOR 0 = 1    => Commutative

(0 XOR 1) XOR 1 =1 XOR 1 = 0               0 XOR(1 XOR 1) = 0 XOR 0 =0        => Associative

D. NAND

0 NAND 1 = 1 NAND 0 =1    => Commutative

(0 NAND 1)NAND 1 = 1 NAND 1 =0                  0 NAND (1 NAND 1) = 0 NAND 0 = 1  => Not associative

• Every logic gate follows Commutative law
• AND,OR,Ex-OR,EX-NOR follows Associative law. NAND,NOR doesn`t follow Associative law.
• AND ,OR follows Distributive law.Ex-OR,EX-NOR,NAND,NOR doesn`t follow Distributive law.

Answer 2

commutative means A op B = B op A for all values of A and B.

associative means (A op B) op C = A op (B op C) for  all values of A , B, and C.

the above rules are applied on OR, NOR, EX-OR, NAND operations. Then finally conclude that NOR and NAND both operations are commutative but not associative.

Comments

NAND is not associative