If ⊕ represents XOR Gate in Boolean algebra and A ⊕ B = C, then B ⊕ C equals to:

Correct option is B

In Boolean algebra, the XOR (Exclusive OR) operation has the following properties:
1. XOR Definition:
· A ⊕ B = C means that the result of A XOR B is C.
· The XOR operation produces 1 if the number of 1s in the operands is odd; otherwise, it produces 0.
Now, the expression we are interested in is:
B ⊕ C.
Since A ⊕ B = C, we can substitute C in terms of A and B:
B ⊕ (A ⊕ B).
We use the property of XOR: B ⊕ (A ⊕ B) = A.
This is because XOR is commutative and associative, and we can think of it as undoing the XOR operation between B and A ⊕ B, thus returning the original A.
Important Key Points:
1. XOR Inverse Property: XOR of a number with itself (e.g., A ⊕ A) results in 0. So, when we XOR B with A ⊕ B, the result is simply A.
2. Commutative and Associative Properties: XOR operations satisfy both of these properties, allowing for flexible rearrangement of operands.
Knowledge Booster:
· Option (a): 1 is incorrect because XOR does not simply result in 1 when applied to B and C.
· Option (c): A' is incorrect because the result is A, not the negation of A.
· Option (d): 0 is incorrect because the result of XORing B and C is A, not 0.