NIMCET 2022 — Computer PYQ

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Question

NIMCET 2022 — Computer PYQ

NIMCET | Computer | 2022

Write the simplified form of the Boolean expression (A+C) (A+AD)+AC+C

Choose the correct answer:

Explanation

To simplify the expression, we will apply Boolean laws step-by-step:

Step 1: Simplify the term $(A+AD)$ using the Absorption Law.

According to the Absorption Law, $A + AB = A$ . Therefore:

(A + AD) = A

Step 2: Substitute this back into the original expression.

(A + C)(A) + AC + C

Step 3: Distribute $A$ over $(A+C)$ .

(A \cdot A) + (A \cdot C) + AC + C

Step 4: Use the Idempotent Law ( $A \cdot A = A$ ).

A + AC + AC + C

Since $AC + AC = AC$ :

A + AC + C

Step 5: Apply the Absorption Law again ( $A + AC = A$ ).

A + C

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