A Level Computer Science OCR Practice Exam

Absorption in boolean algebra is represented by which of the following?

1. Av(A AND B) ≡ A

2. A AND (A OR B) ≡ A

3. Av¬A ≡ True

4. Both A and B

The correct answer is: Both A and B

Absorption is a key concept in Boolean algebra that showcases how certain expressions can reduce to simpler forms. The principle of absorption states that combining a variable with a function of itself leads to the original variable. The first expression states that A OR (A AND B) simplifies down to A. This holds true because if A is true, then the entire expression is true regardless of B's value since A is already true. If A is false, then both A OR (A AND B) evaluates to false, which shows that the expression does indeed reduce to A. The second expression, A AND (A OR B), also simplifies to A. Here, if A is true, the whole expression will resolve to true, whereas if A is false, the entire expression is false. Thus, the result is again A. Since both expressions correctly demonstrate the absorption law, the correct choice encompasses both of these representations, highlighting the overarching rule that applies in both cases. Therefore, the conclusion that both formulations accurately depict absorption in Boolean algebra is justified and reinforces the importance of understanding these simplifications in logic programming and circuit design.