In Boolean algebra, A·(A + B) is logically equivalent to:

Correct option is D

In Boolean algebra, the expression A · (A + B) simplifies to A based on the Distributive Law and Idempotent Law.
Simplification Steps:
1. Distributive Law: $$A \cdot (A + B) = (A \cdot A) + (A \cdot B)$$​​
2. Idempotent Law: $$A \cdot A = A$$​ So, the expression becomes:
​$$A + (A \cdot B)$$​​
3. Absorption Law: $$A + (A \cdot B) = A$$​ This is because A absorbs A · B. If A is true, the entire expression is true, regardless of B.
Thus, the expression simplifies to A.
Important Key Points:
1. Distributive Law: $$A \cdot (A + B) = A \cdot A + A \cdot B$$​​
2. Idempotent Law: $$A \cdot A = A$$​​
3. Absorption Law: $$A + (A \cdot B) = A$$​​
Knowledge Booster:
· Option (a): B is incorrect. The simplified expression is A, not B.
· Option (b): A · B is incorrect because we don't end up with a product of A and B in this simplification.
· Option (c): A + B is incorrect because the result of the simplification is A, not A + B.