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Express the following switching circuit in the symbolic form of logic. Construct the switching table :[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'\…

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

[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 lamp L and a battery.]

Doubtly Asked Board exam · March 2024 hsc 12th Save WhatsApp Report
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Answer: Symbolic form \((p \vee q) \wedge \sim p \wedge \sim q\); 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 \(\sim p\): \(S_1'\) is closed and \(\sim q\): \(S_2'\) is closed.

\(S_1\) and \(S_2\) are in parallel: \(p \vee q\). This is in series with \(S_1'\) and \(S_2'\). So the symbolic form is \((p \vee q) \wedge \sim p \wedge \sim q\).

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

The last column contains only 0, so the lamp will not glow for any position of the switches.

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report
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