NIMCET 2022 — Computer PYQ

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Question

NIMCET 2022 — Computer PYQ

NIMCET | Computer | 2022

Which of the following is equivalent to the Boolean expression $(X + Y)$ . $(X + \overset{ˉ}{Y}) . (\overset{ˉ}{X} + Y)$

Choose the correct answer:

Explanation

To solve this, we simplify the expression step-by-step using Boolean algebra rules.

Step 1: Simplify the first two terms $(X + Y) \cdot (X + \bar{Y})$ .

Applying the Distributive Law ( $A+BC = (A+B)(A+C)$ ):

(X + Y) \cdot (X + \bar{Y}) = X + (Y \cdot \bar{Y})

Step 2: Use the Complement Law ( $Y \cdot \bar{Y} = 0$ ).

X + 0 = X

Step 3: Multiply the result by the third term $(\bar{X} + Y)$ .

X \cdot (\bar{X} + Y)

Step 4: Distribute $X$ over the parentheses.

(X \cdot \bar{X}) + (X \cdot Y)

Step 5: Use the Complement Law again ( $X \cdot \bar{X} = 0$ ).

0 + XY = XY

\therefore \text{Correct Option: } \mathbf{A}