Question

Given below are two statements.
Assertion (A):
If \(A\) and \(B\) are two Boolean terms, then \(A+AB=A\).
Reason (R):
\(x+xy=x\) is absorption law in Boolean Algebra.

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Absorption laws are \(A+AB=A\) and \(A(A+B)=A\).

Answer 1

The Correct Option is A

Concept:
Boolean algebra follows absorption law: \[ x+xy=x \]

Step 1: Given expression. \[ A+AB \]

Step 2: Take \(A\) common. \[ A+AB=A(1+B) \]

Step 3: Use Boolean identity. \[ 1+B=1 \] So, \[ A(1+B)=A\cdot1=A \] Thus, \[ A+AB=A \] Reason gives the same absorption law. Hence, both Assertion and Reason are correct, and Reason explains Assertion. \[ \therefore \text{Correct Answer is (A)} \]