GATE CS 2019 Set 1 — Question 16
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Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems
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Question
Which one of the following is NOT a valid identity?
Correct answer
(B) (x + y) ⊕ z = x ⊕ (y + z)
Solution
Let's analyze each option:(A) : This is the associative property of XOR. It is valid.(B) : Let's test with values. Let .
LHS: .
RHS: .
Since , this identity is NOT valid.(C) , if : If , it means and are not both 1. The XOR operation is . If , then behaves exactly like XOR (no carry/overlap). Valid.(D) : The expression represents XNOR (). The complement of XNOR is XOR. Valid.The question asks for the one that is NOT a valid identity.
Answer: (B).
LHS: .
RHS: .
Since , this identity is NOT valid.(C) , if : If , it means and are not both 1. The XOR operation is . If , then behaves exactly like XOR (no carry/overlap). Valid.(D) : The expression represents XNOR (). The complement of XNOR is XOR. Valid.The question asks for the one that is NOT a valid identity.
Answer: (B).
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