The image contains multiple choice questions on various topics related to Information and Communication Technology. We are asked to solve question 9: "The logic circuit equivalent to $A(A+B)$ is?"

1. Problem Description

The image contains multiple choice questions on various topics related to Information and Communication Technology. We are asked to solve question 9: "The logic circuit equivalent to $A(A+B)$ is?"

2. Solution Steps

We need to find the logic circuit that represents the Boolean expression $A(A+B)$. Let's simplify this expression using Boolean algebra.

$A(A+B) = A*A + A*B$ (Distributive Law)

$A*A = A$ (Idempotent Law)

So, $A(A+B) = A + AB$.

$A + AB = A(1+B)$ (Factoring out A)

$1 + B = 1$ (Since ORing anything with 1 results in 1)

Thus, $A(A+B) = A(1) = A$.

Now we need to find a logic circuit whose output is A. In other words, the output should directly follow the input A.

Option (3) shows a direct connection from A to the output, which matches the simplified expression.

3. Final Answer

(3)