Boolean Algebra

The given boolean expression is: Let's simplify it step-by-step: - First, notice that the expression can be grouped as follows: - From the **complement law**: , so the expression becomes: - Now, we use the **absorption law**: . Thus, the simplified expression is: Hence, the correct output is **(4) **.

Step 1: K-map Simplification.
Looking at the given K-map, the minimal function is derived by grouping the ones and simplifying the terms based on the groupings. The grouping results in the minimal function: - from the top left corner group. - from the second row. - from the second column group.

Step 2: Conclusion.
The correct minimal function is ** **.

Step 1: Understanding the Concept:
Boolean Algebra deals with binary variables and logic gates. Unlike standard algebra, it follows specific laws like Idempotent, Commutative, and Distributive laws, where variables can only take values of 0 or 1.
Step 2: Detailed Explanation:
Let's examine each option:
- Option A: This is the Commutative Law for addition (OR). It is a valid property.
- Option B: This is the Distributive Law where AND distributes over OR. It is a valid property.
- Option D: This is the second Distributive Law unique to Boolean Algebra where OR distributes over AND. It is a valid property.
- Option C: According to the Idempotent Law, . In Boolean logic, there is no concept of a coefficient "2" because the result of any logical OR of a variable with itself is simply the variable itself.
Step 3: Final Answer:
The expression is mathematically incorrect in the context of Boolean Algebra.