ITPEC FE Morning April 2021 Question 1
ITPEC FE Morning April 2021 — Question 1 of 80
Boolean Algebra — Distributive & Absorption Laws — simplify (x + y) · (x + z).
Expand using the distributive law:
(x + y) · (x + z) = x·x + x·z + y·x + y·z
Apply idempotent law (x · x = x):
= x + x·z + x·y + y·z
Apply absorption law (x + x·A = x):
- •
x + x·z = x - •
x + x·y = x
Result: x + y·z
Why not others:
- (a) x · (y + z) — equals x·y + x·z, missing standalone x
- (c) x·y + y·z — missing standalone x
- (d) (x̄ + y) · z — uses NOT x, completely different expression
Key rule: Absorption law: x + x·A = x. If x = 1, the entire OR is already 1 regardless of A.
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