Question

In a Boolean Algebra $p \vee p$ is is equal to

• A. 1
• B. 0
• C. 2
• D. none of these

Hint:

The Idempotent laws (\(A+A=A\) and \(A \cdot A=A\)) are fundamental in simplifying Boolean expressions. They mean that repeating a term in an OR or AND operation has no effect on the outcome.

Answer 1

The Correct Option is D

Step 1: Identify the Boolean law. The expression \text{$p \vee p$ } (p OR p) represents the Idempotent Law of Boolean algebra.
Step 2: Apply the Idempotent Law. The law states that for any Boolean variable p, \text{$p \vee p$ = p} and \text{$p \wedge p$ = p}. The result of OR-ing a variable with itself is the variable itself.
Step 3: Evaluate the given options. The result is \text{p}. The options are constant values: 1, 0, and 2. None of these is equal to \text{p} in the general case. For example, if p=0, $p \vee p$ =0. If p=1, $p \vee p$ =1. Since the result depends on the value of p and is not a constant, none of the options A, B, or C are correct. Option (C) 2 is not a valid value in Boolean algebra. Therefore, the correct choice is "none of these".