MHT CET · Maths · Mathematical Reasoning
For the circuit show below, the Boolean polynomial is
- A \((\sim p \vee q) \vee(p \vee \sim q)\)
- B \((\sim p \wedge q) \wedge(p \wedge q)\)
- C \((\sim p \wedge \sim q) \wedge(q \wedge p)\)
- D \((\sim p \wedge q) \vee(p \wedge \sim q)\)
Answer & Solution
Correct Answer
(D) \((\sim p \wedge q) \vee(p \wedge \sim q)\)
Step-by-step Solution
Detailed explanation
Since, \(\sim p\) and \(q\) both switch also are in series
\(
\Rightarrow (\sim p \wedge q)
\)
and \(p\) and \(\sim q\) both switch also are in series
\(
\Rightarrow (p \wedge \sim q)
\)
Both Eqs. (i) and (ii) are parallel switch
\(
\Rightarrow (\sim p \wedge q) \vee(p \wedge \sim q)
\)
\(
\Rightarrow (\sim p \wedge q)
\)
and \(p\) and \(\sim q\) both switch also are in series
\(
\Rightarrow (p \wedge \sim q)
\)
Both Eqs. (i) and (ii) are parallel switch
\(
\Rightarrow (\sim p \wedge q) \vee(p \wedge \sim q)
\)
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