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: Understanding the Concept
In Boolean algebra the plus sign means logical OR. The expression \(Y=A+B\) describes an OR gate.

Step 2: Truth table
\[ \begin{array}{cc|c}A&B&Y\\0&0&0\\0&1&1\\1&0&1\\1&1&1\end{array} \]

Step 3: Reading the table
Y is 1 whenever A is 1, or B is 1, or both are 1. It is 0 only when both inputs are 0.

Step 4: Check the options
(A) describes XOR, which excludes the case of both. (B) describes AND. (C) describes NOR. (D) describes OR, which matches.

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