Which Boolean Law is represented in the following? P = P + P · Q

Concept: The Absorption Law in Boolean Algebra states that for any two variables A and B: A + A·B = A (and dually, A·(A + B) = A). When a variable is combined with its own product with another term, that extra term is redundant, because the variable itself already guarantees the result — so the expression always collapses back to the original variable.

Application: Apply this law to the given identity P = P + P · Q.

1. Start from the right-hand side: P + P · Q.

2. Factor P out using the Distributive Law: P + P · Q = P · (1 + Q).

3. By the Identity Law for OR, 1 + Q = 1 for every value of Q.

4. Substitute: P · (1 + Q) = P · 1.

5. By the Identity Law for AND, P · 1 = P.

6. So P + P · Q simplifies to P, exactly matching the left-hand side — this is precisely the pattern the Absorption Law defines.

Cross-check: Verify with truth values. If P = 1, then P + P·Q = 1 + Q = 1 = P for every Q. If P = 0, then P + P·Q = 0 + 0 = 0 = P for every Q. Both cases confirm P + P·Q = P regardless of Q, matching the Absorption Law.

Contrast with the other laws:

• Distributive Law has the form A·(B + C) = A·B + A·C — it distributes a term over a sum; on its own it does not collapse an expression back to a single variable.

• Associative Law only regroups terms, e.g. (A + B) + C = A + (B + C) — it does not reduce the number of distinct terms involved.

• De Morgan's Law converts a negated AND/OR into complement form, e.g. ¬(A·B) = ¬A + ¬B — it involves negation, which is absent from P = P + P·Q.

Hence, the equation P = P + P · Q represents the Absorption Law.