Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

(A) A
(B) B
(C) C
(D) D


Answer: (D)

Explanation: (A) (p⊕q)\’ = (pq\’ + p\’q)\’ = (p\’+q).(p+q\’) = (pp\’ +p\’q\’ + qp + qq\’) = pq + p\’q\’ = (p⊙q)
(B) (p\’)⊕q = (p\’)q\’ + (p\’)\’q = pq + p\’q\’ = (p⊙q)
(C) (p\’⊕q\’) = (p\’)\’.(q\’) + (p\’).(q\’)\’ = p.(q\’) + (p\’).q = p⊕q.
(D) (p⊕(p\’))⊕q =(pp\’\’+ p\’p\’)⊕q =(p+p\’)⊕q = 1⊕q = 1.q\’ + 0.q = q\’
And
(p⊙(p\’))⊙(q\’) = (pp\’ + p\’.p\’\’)⊙(q\’) = 0⊙(q\’) = 0(q\’) + 1.(q\’)\’ = q

Please note that (p⊕q) = (p\’⊙q) = (p⊙q\’) = (p\’⊙q\’)\’ but not (p\’⊙q\’).
Similarly, (p⊙q) = (p\’⊕q) = (p⊕q\’) = (p\’⊕q\’)\’ but not (p\’⊕q\’).

So, option (D) is false.


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