Which of the following is not a valid Boolean algebra rule?

A Boolean algebra rule is valid only if both sides of the equation match for every possible 0/1 assignment to its variables. Standard laws include the idempotent law (A·A = A), the absorption law ((A+B)·A = A), the absorption-type identity (A′ + AB = A′ + B), and the distributive law ((A+B)·(A+C) = A+BC).

1. Apply the absorption-type identity A′ + AB = A′ + B with A = X: X̄ + XY reduces to X̄ + Y, not to Y.

2. X̄ + Y equals Y for every Y only when X̄ = 0 (that is, X = 1); the option claims the equality for ALL X and Y, so it cannot be a general Boolean law.

3. Checking the remaining rules the same way: X·X = X holds for every X (idempotent law); (X+Y)·X = X holds for every X, Y (absorption law); (X+Y)·(X+Z) = X+YZ holds for every X, Y, Z (distributive law).

A direct substitution confirms the failure: with X = 0 and Y = 0, the left side of X̄ + XY becomes 1 + (0·0) = 1, while the right side, Y, is 0 — the two sides disagree, so the rule does not hold in general.

So the equality X̄ + XY = Y is the one that fails to be a valid Boolean algebra identity, while the other three rules are all valid Boolean laws (idempotent, absorption, and distributive).