UGC-NET | UGC NET CS 2016 July – II | Question 6

Which of the following logic expressions is incorrect?
(A) 1 ⊕ 0 = 1
(B) 1 ⊕ 1 ⊕ 1 = 1
(C) 1 ⊕ 1 ⊕ 0 = 1
(D) 1 ⊕ 1 = 0


Answer: (C)

Explanation: We know that x ⊕ y = x`y + xy`
So,

  1. 1 ⊕ 0 = 1`0 + 10` = 0 * 0 + 1 * 1 = 0 + 1 = 1
  2. 1 ⊕ 1 ⊕ 1 = (1 ⊕ 1) ⊕ 1 = (1`1 + 11`) ⊕ 1 = (0) ⊕ 1 = 1`0 + 10` = 0 * 0 + 1 * 1 = 0 + 1 = 1
  3. 1 ⊕ 1 ⊕ 0 = 1 ⊕ (1 ⊕ 0 ) = 1 ⊕ ( 1`0 + 10` = 0 * 0 + 1 * 1 = 0 + 1 ) = 1 ⊕ 1 = 1`1 + 11` = 0
  4. 1 ⊕ 1 = 1`1 + 11` = 0
  5. So, option (C) is correct.

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