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(A) The given circuit consists of two switches $S_1$ and $S_2$ in parallel. Let $p$ be the statement that switch $S_1$ is closed and $q$ be the statem

Vedclass · Accepted Answer

$[(p 	o q) \land \sim q] 	o \sim p$

Vedclass · Answer

(A) The given circuit consists of two switches $S_1$ and $S_2$ in parallel. Let $p$ be the statement that switch $S_1$ is closed and $q$ be the statement that switch $S_2$ is closed.Since the switches are in parallel, the logical expression for the circuit is $(p \lor q)$.We need to find the equivalent expression among the options.Let's simplify the options:$(A)$ $[(p 	o q) \land \sim q] 	o \sim p \equiv [(\sim p \lor q) \land \sim q] 	o \sim p \equiv [(\sim p \land \sim q) \lor (q \land \sim q)] 	o \sim p \equiv [(\sim p \land \sim q) \lor F] 	o \sim p \equiv (\sim p \land \sim q) 	o \sim p \equiv \sim(\sim p \land \sim q) \lor \sim p \equiv (p \lor q) \lor \sim p \equiv (p \lor \sim p) \lor q \equiv T \lor q \equiv T$.$(B)$ $(p 	o q) \land (p \land \sim q) \equiv (\sim p \lor q) \land (p \land \sim q) \equiv (\sim p \land p \land \sim q) \lor (q \land p \land \sim q) \equiv (F \land \sim q) \lor (p \land F) \equiv F \lor F \equiv F$.$(C)$ $[(p \lor q) \land \sim p] \land \sim q \equiv [(p \land \sim p) \lor (q \land \sim p)] \land \sim q \equiv [F \lor (q \land \sim p)] \land \sim q \equiv (q \land \sim p) \land \sim q \equiv (q \land \sim q) \land \sim p \equiv F \land \sim p \equiv F$.$(D)$ The expression involves $r$, which is not in the circuit.Note: The provided image for the question shows two switches in parallel, which corresponds to $(p \lor q)$. If the question implies finding a circuit that simplifies to a specific logical form, the provided options do not match $(p \lor q)$ directly. However, based on standard logic circuit problems, if the circuit was meant to be $S_1$ and $S_2$ in series, it would be $(p \land q)$. Given the options, there is a mismatch between the circuit diagram and the logical expressions provided.

The simplified switching circuit for the following circuit is

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The contrapositive of $(\sim p \wedge q) \rightarrow (q \wedge \sim r)$ is

The dual of $(x \vee y) \wedge (x \vee 1) = x \vee (x \wedge y) \vee y$ is

Which of the following statements is/are False?
$S_1 : \exists n \in N$, such that $n^2 + n + 2$ is divisible by $4$.
$S_2 : \exists x \in N$, such that $x - 17 < 20$.
$S_3 : \forall n \in N, n^2 + 3n - 10 = 0$.
$S_4 : \forall n \in N, n^2 \ge 1$.

Which of the following statement patterns is a tautology?
$S_{1} \equiv \sim p \rightarrow (q \leftrightarrow p)$
$S_{2} \equiv \sim p \vee \sim q$
$S_{3} \equiv (p$ $\rightarrow q) \wedge (q$ $\rightarrow p)$
$S_{4} \equiv (q \rightarrow p) \vee (\sim p \leftrightarrow q)$

Which one of the following statements is not a tautology?

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