The simplified switching circuit for the foll | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

The contrapositive of the statement "If you are born in India,then you are a citizen of India" is:

The contrapositive of $\sim q \to p$ is equivalent to

If $p \Rightarrow (\sim p \vee q)$ is false,the truth values of $p$ and $q$ are respectively

Show that the statement "For any real numbers $a$ and $b$,$a^{2}=b^{2}$ implies that $a=b$" is not true by giving a counter-example.

Vedclass Test Series

Exam Paper Generator

Online Exam Module