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NIMCET 2011 Computer PYQ — Consider and be some Boolean variables, denotes the OR operation … | Mathem Solvex | Mathem Solvex

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NIMCET 2011 — Computer PYQ

NIMCET | Computer | 2011

Consider $x$ and $y$ be some Boolean variables, $+$ denotes the OR operation and $“.”$ denotes the AND operation. What will be the simplified form of the Boolean expression : $x . (x + y)$ ?

Choose the correct answer:

A.
y
B.
1
C.
0
D.
x
(Correct Answer)

Correct Answer:

Explanation

Solution:

Given expression: $x \cdot (x + y)$
Apply Distributive Law: $(x \cdot x) + (x \cdot y)$
Apply Idempotent Law ( $x \cdot x = x$ ): $x + (x \cdot y)$
Apply Absorption Law ( $x + xy = x$ ): $x$

Correct Option: (d)

Explanation

Solution:

Given expression: $x \cdot (x + y)$
Apply Distributive Law: $(x \cdot x) + (x \cdot y)$
Apply Idempotent Law ( $x \cdot x = x$ ): $x + (x \cdot y)$
Apply Absorption Law ( $x + xy = x$ ): $x$

Correct Option: (d)

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