Question on Logical expressions

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

(A) xy  + x 'y '
(B) x  ⊕ y '
(C) x ' ⊕ y
(D) x ' ⊕ y '

Answer : (D)

Explanation :

Elimination Method

Option A : xy + x'y' => This is nothing but (x NOR y)

Option B : x ⊕ y' = x(y')'+x'(y') = xy+x'y' = X NOR y

Option C: x' ⊕ y = x'(y)'+(x')'y =x'y'+xy= X NOR y

Option D:  x ' ⊕ y ' = x'(y')'+(x')'y'=x'y+xy' = x ⊕ y <> x NOR y

So, answer is D.

Truth Table Method
Lets write truth tables for each of those expressions.

Truth tables for the expressions in question :

As you can see, except expression in (D), all expressions match x NOR y. So, answer is (D)

Topics to revise :
Logical Expressions
Truth Tables

References :