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Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$?

1. $xy + x′ y′$
2. $x\oplus y′$
3. $x′\oplus y$
4. $x′\oplus y′$

$A$ : means both are either true OR both are false. then it will be true = ExNOR

$B$ & $C$ : whenever any one of the literal is complemented then ExOR can be turned to ExNOR and complement sign on the literal can be removed. So these two also represents ExNOR operation of $x$ and $y$.

Answer is option D. It is the ExOR operation b/w the two.

edited
The exclusive NOR  and exclusive OR of x and y is given by the expressions

x⊙y = x.y + x'.y' (exclusive NOR or XNOR)

x⊕y = x'.y + x.y' (exclusive OR or XOR)

So (A) is automatically true.

(B) is x⊕y' which evaluates to x'.y' + x.(y')' (as per the formula above for XOR) = x'.y' + x.y which is equivalent to x⊙y.

(C) is x'⊕y which evaluates to (x')'.y + x'.y' (as per the formula above for XOR) = x.y + x'.y' which is equivalent to x⊙y.

(D) is x'⊕y' which evaluates to (x')'.y' + x'.(y')' (as per the formula above for XOR) = x.y' + x'.y which is NOT equivalent to x⊙y.

Hence D is FALSE.

(D) x'y'

X nor Y when both X=Y=0 then X nor Y =1

A) xy + x' y' = 1

B)x ex-or y' = xy + x'y'

C)x' ex-or y = x'y' + x y

D)x' ex-or y' = x' y + x y'

So option D is correct
+1 vote
simplest one !

put the value x= 1 y=1 z =1 and put in all the options, you will get d is giving value 0 and our main equation which is mention in the question is giving value 1 so the equation which does not belong to answer is option d >

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