Question

In Boolean expression \(A+B = Y\) implies that

• A. \(Y\) exists when \(A\) or \(B\) exists but not when both \(A\) and \(B\) exist.
• B. \(Y\) exists only when \(A\) and \(B\) both exist.
• C. \(Y\) exists when both \(A\) and \(B\) do not exist.
• D. \(Y\) exists when \(A\) exists or \(B\) exists or both \(A\) and \(B\) exist

Hint:

A plus sign in Boolean algebra is the OR operation.

Answer 1

The Correct Option is D

Step 1: Approach
Test the four input pairs.

Step 2: Test
00 gives 0. 01 gives 1. 10 gives 1. 11 gives 1 (since $1+1=1$ in Boolean algebra).

Step 3: Answer
The output exists when A exists, or B exists, or both exist. Option (D).

Final Answer:
Y is 1 when A, or B, or both are 1, so it is an OR gate, option (D). \[ \boxed{\text{Y exists when A or B or both exist}} \]