Explanation:
In logic design, simplification of logic expressions can often be achieved by using basic logic operations such as XOR and X-NOR. The given question asks us to identify the operation that can be used alongside XOR for simplification.

XOR Operation:
The XOR (exclusive OR) operation is a binary operation that takes two inputs and produces a true output when the number of true inputs is odd. It produces a false output when the number of true inputs is even. The XOR operation can be represented by the symbol ⊕.

X-NOR Operation:
The X-NOR (exclusive NOR) operation is a binary operation that produces a true output when the number of true inputs is even. It produces a false output when the number of true inputs is odd. The X-NOR operation can be represented by the symbol ⊙.

Simplification using XOR and X-NOR:
Both XOR and X-NOR operations can be used for simplification of logic expressions. However, the question specifically asks for the operation that can be used alongside XOR for simplification. The correct answer is X-NOR (option A).

Explanation:
Using XOR and X-NOR operations together, we can simplify logic expressions in the following ways:

1. XOR and X-NOR complement each other: The output of an XOR operation is the complement of the output of an X-NOR operation, and vice versa. Therefore, if we have an expression involving XOR and X-NOR operations, we can simplify it by replacing one operation with the other.

2. XOR and X-NOR are associative: The XOR and X-NOR operations are associative, meaning that the order in which these operations are performed does not affect the result. Therefore, we can rearrange the order of operations to simplify the expression.

3. XOR and X-NOR can be combined: In some cases, we can combine XOR and X-NOR operations to simplify the expression further. For example, we can use De Morgan's law to convert an X-NOR operation into an XOR operation, and vice versa.

Therefore, by using XOR and X-NOR operations together, we can simplify logic expressions and reduce the complexity of the circuit. This can lead to improved performance, reduced power consumption, and easier circuit design.