Simplify the given circuit by writing its logical expression. Also write your conclusion. ![Circuit diagram: switch S1 in series leads into two parallel branches — top branch has switch S1', bottom branch has switch S2' — which — Class 12 Mathematics question](/figures/mh-math-mathematical-logic/circuit-switch-series-leads-two-parallel-branches-fig-pyq-hgnzjj.svg)

Simplify the given circuit by writing its logical expression. Also write your conclusion.

Question 215 of 227

Q. Simplify the given circuit by writing its logical expression. Also write your conclusion.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2023Subjective· 4mImportance★★★★★

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Let $p=S_1,\ q=S_2$ ; expression $=p\wedge(p'\vee q')\wedge q$ reduces to a contradiction.

From the figure: $S_1$ in series with the parallel combination of $S_1'$ and $S_2'$ , in series with $S_2$ .

Let $p=S_1$ , $q=S_2$ . Logical expression: $L=p\wedge(p'\vee q')\wedge q$

$=(p\wedge q\wedge p')\vee(p\wedge q\wedge q')$ [distributing]

$=((p\wedge p')\wedge q)\vee(p\wedge(q\wedge q'))$

$=(F\wedge q)\vee(p\wedge F)$ [since $p\wedge p'=F,\ q\wedge q'=F$ ]

$=F\vee F=F$

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