Which of the following represents Absorption Law correctly?
2023
Which of the following represents Absorption Law correctly?
Answer: B. X+YX=X — Absorption laws in Boolean algebra: X + X·Y = X — Derivation: X + X·Y = X(1+Y) = X·1 = X. X·(X+Y) = X — Derivation: X·(X+Y) = X·X + X·Y = X + X·Y = X. Which…
- A.
X+Y.Z=(X+Y)(X+Z)
- B.
X+YX=X
- C.
(X+Y)'=X'Y'
- D.
(X.X)'=X'
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Correct answer: B
Absorption laws in Boolean algebra:
X + X·Y = X — Derivation: X + X·Y = X(1+Y) = X·1 = X.
X·(X+Y) = X — Derivation: X·(X+Y) = X·X + X·Y = X + X·Y = X.
Which provided statement matches absorption: the statement that reads "X+YX=X" (i.e., X + X·Y = X) is the absorption law and is correct. The statement "X+Y·Z=(X+Y)(X+Z)" is the distributive law; "(X+Y)'=X'Y'" is De Morgan's law; and "(X·X)'=X'" follows from idempotence then complement. Therefore the correct absorption identity among the choices is the one stating X + X·Y = X.