Discussion
The Boolean expression \((\overline{AB})(\bar{A} + B)(A + \bar{B})\) can be simplified to
Answer: C
The expression simplifies to \(\overline{A + B}\).
First multiply the last two factors:
\[ \begin{aligned} (\bar{A} + B)(A + \bar{B}) &= \bar{A}\bar{B} + AB \\ \overline{AB}\,(\bar{A}\bar{B} + AB) &= (\bar{A} + \bar{B})\bar{A}\bar{B} + 0 \\ &= \bar{A}\bar{B} = \overline{A + B} \end{aligned} \]
The product \(\overline{AB}\cdot AB\) is zero, leaving only \(\bar{A}\bar{B}\), which by De Morgan's law is the NOR \(\overline{A + B}\). Checking with \(A = B = 1\): the expression is 0, which rules out \(A + B\) and \(AB\); with \(A = 0, B = 1\) it is 0, which rules out \(\bar{A}B\).
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development