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

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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.
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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.
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