NIMCET 2015 — Computer PYQ

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Question

NIMCET 2015 — Computer PYQ

NIMCET | Computer | 2015

Which of the following is equivalent to the expression $\overline{(\overline{X + Y} + Z)}$ ?

Choose the correct answer:

Explanation

simplification:

Given expression:

F = \overline{(\overline{X + Y} + Z)}

Step 1: Apply De Morgan's Law to the outermost complement. Treat $(\overline{X + Y})$ as $A$ and $Z$ as $B$ .

\overline{A + B} = \bar{A} \cdot \bar{B}

So,

F = \overline{(\overline{X + Y})} \cdot \bar{Z}

Step 2: Apply the Double Complement Law, which states that $\overline{\bar{A}} = A$ .

\overline{(\overline{X + Y})} = X + Y

Step 3: Substitute this back into the expression.

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

Conclusion: The simplified expression is $(X + Y)\bar{Z}$ .

The correct option is (b).