MHT CET20255 May 2025Evening ShiftMathematicsMathematical ReasoningActual
If p : switch s ₁ is closed, q : switch s ₂ is closed then correct interpretation from the following circuit is
Options
- AThe lamp is always on
- BThe lamp is always off
- CSymbolic form is p ( p q ) q
- Dis equivalent to p q
Correct answer
B. The lamp is always off
Step-by-step solution
Interpretation: Represent switch S1 closed as p and S2 closed as q , with S1' as p and S2' as q . The lamp glows when there is a complete conductive path. The circuit consists of S1 in series with a parallel combination of S1' and S2', followed by S2 in series. The condition for the lamp to be on is p ( p q) q . Simplifying the expression: p ( p q) = (p p) (p q) = F (p q) = p q Substituting gives (p q) q = p ( q q) = p F = F . The expression simplifies to false, indicating the lamp never glows regardless of switch