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Express the following switching circuit in the symbolic form of logic. Construct the switching table and interpret it:[Figure: Switches \(S_1\) and \(S_2\) are connected in parallel; this parallel combination is connected in series with switches \(S_…

Q.15 Express the following switching circuit in the symbolic form of logic. Construct the switching table and interpret it:

[Figure: Switches \(S_1\) and \(S_2\) are connected in parallel; this parallel combination is connected in series with switches \(S_1'\) and \(S_2'\), a battery and a lamp L.]

Doubtly Asked Board exam · March 2025 hsc 12th Save WhatsApp Report
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Answer: \((p \vee q) \wedge \sim p \wedge \sim q\); the final column is all 0, so the lamp never glows.

Let \(p\): switch \(S_1\) is closed, \(q\): switch \(S_2\) is closed. Then \(S_1'\) and \(S_2'\) correspond to \(\sim p\) and \(\sim q\).

Symbolic form: \((p \vee q) \wedge (\sim p) \wedge (\sim q)\).

\(p\)\(q\)\(p \vee q\)\(\sim p\)\(\sim q\)\((p \vee q) \wedge \sim p \wedge \sim q\)
111000
101010
011100
000110

Interpretation: The last column contains only 0, so the lamp will not glow whatever the positions of the switches \(S_1\) and \(S_2\) (the statement pattern is a contradiction).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report
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