GATE CS 1987 Q12-a — Boolean Algebra

The XOR ($\oplus$) operator is both commutative and associative. This allows us to rearrange the terms in the given Boolean expression:

Using the properties of the XOR operator:

1. Self-inverse property: Any variable XORed with itself results in $0$.
   $A \oplus A = 0$
2. Identity property: Any variable XORed with $0$ remains unchanged.
   $0 \oplus B = B$

Substituting these properties into the expression:

Thus, the expression is equivalent to $B$, which corresponds to option C.