Boolean Algebra and Logical Operations

Boolean algebra is a mathematical structure that deals with binary variables and logical operations. It is named after mathematician George Boole, who developed the algebraic system in the mid-19th century. Boolean algebra is widely used in computer science and digital electronics to express and simplify logical expressions.

In Boolean algebra, logical operations are performed on binary variables, which can take on one of two values: true (represented as 1) or false (represented as 0). These logical operations include AND, OR, and NOT.

AND Operation

The AND operation is denoted by a dot (.) or an asterisk (*) in Boolean algebra. It returns true (1) only if both operands are true (1), otherwise it returns false (0).

For example, if we have two binary variables A and B, the AND operation (A . B) will be true (1) only if both A and B are true (1). Otherwise, it will be false (0).

Using AND Operation in Boolean Algebra

Let's consider the expression (A . A) A. This expression involves the AND operation between A and A, followed by another AND operation between the result and A.

When we perform the AND operation between A and A, we get the same value as A. This is because both operands are the same, and the AND operation returns true (1) only when both operands are true (1).

Thus, (A . A) evaluates to A.

Next, we perform the AND operation between the result (A) and A. Again, since both operands are the same, the result will be A.

Therefore, the expression (A . A) A simplifies to A.

Answer: A

Hence, the correct answer is option 'A', which states that (A . A) A evaluates to A.