Question:
Simplify the Boolean expression using Boolean algebra laws:
\(F = A B + A (B + C) + B (B + C)\)
बूलियन बीजगणित के नियमों का उपयोग करके व्यंजक को सरल बनाएं:
\(F = A B + A (B + C) + B (B + C)\)
Options:
- B + AC
- A + BC
- AB + C
- B + C
- B + AC
- A + BC
- AB + C
- B + C
Correct Answer: a)
Explanation:
Expand the expression:
\(F = AB + AB + AC + B\cdot B + BC\)
Since \(AB + AB = AB\) and \(B\cdot B = B\):
\(F = AB + AC + B + BC\)
Group terms with \(B\): \(B(A + 1 + C) + AC\)
Since \(1 + \text{anything} = 1\), \(B(1) + AC = \textbf{B + AC}\) (Option a).
विस्तार करने पर: \(F = AB + AC + B + BC = B(A + 1 + C) + AC = \textbf{B + AC}\) (विकल्प a)।