In Boolean algebra, (A.A) + A =?a)Ab)0c)Ad)1Correct answer is option 'A'. Can you explain this answer?

Question

Answer

(A.A̅) + A
= 0 + A = A
All Boolean algebra laws are shown below:

Answer

Explanation:
Boolean algebra is a mathematical structure used to represent and manipulate binary variables and their logical operations. It is based on the principles of logic and is widely used in digital electronics and computer science.

In Boolean algebra, there are three basic operations: AND, OR, and NOT. These operations are represented by the symbols '.', '+', and ''', respectively.

The given expression is (A.A) A. Let's break it down step by step to simplify and evaluate the expression:

Step 1: Simplify the expression inside the parentheses using the AND operation.

(A.A) = A

This simplification is based on the fact that the AND operation between two identical variables always results in the same variable. If A is true, then A.A is also true. If A is false, then A.A is also false.

Step 2: Substitute the simplified expression back into the original expression.

(A.A) A = A.A

Step 3: Simplify the expression using the AND operation.

A.A = A

This simplification is based on the fact that the AND operation between a variable and itself always results in the same variable. If A is true, then A.A is also true. If A is false, then A.A is also false.

Step 4: Substitute the simplified expression back into the original expression.

(A.A) A = A

Therefore, the final simplified expression is A.

Conclusion:
In Boolean algebra, the expression (A.A) A simplifies to A. This means that the value of the expression is always the same as the value of the variable A. So, the correct answer is option 'A'.

Answer

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.

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