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प्रश्न
The logically equivalent statement of \[\left(\sim p\wedge q\right)\vee\left(\sim p\wedge\sim q\right)\] \[\vee\left(\ p\wedge\sim q\right)\] is
विकल्प
\[(\sim p)\wedge q\]
\[(\sim p)\lor(\sim q)\]
\[(\sim p)\wedge(\sim q)\]
\[\ p\lor\ q\]
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उत्तर
\[(\sim p)\lor(\sim q)\]
Explanation:
\[(\sim\mathrm{p}\wedge\mathrm{q})\vee(\sim\mathrm{p}\wedge\sim\mathrm{q})\vee(\mathrm{p}\wedge\sim\mathrm{q})\]
\[\equiv\sim\mathrm{p}\wedge(\mathrm{q}\vee\sim\mathrm{q})\vee(\mathrm{p}\wedge\sim\mathrm{q})\]
\[\equiv({\sim}\mathrm{p}\wedge\mathrm{T})\vee(\mathrm{p}\wedge{\sim}\mathrm{q})\]
\[\equiv\sim\mathrm{p}\lor(\mathrm{p}\land\sim\mathrm{q})\]
\[\equiv(\sim\mathrm{p}\lor\mathrm{p})\land(\sim\mathrm{p}\lor\sim\mathrm{q})\]
\[\equiv\mathrm{T}\wedge(\sim\mathrm{p}\vee\sim\mathrm{q})\]
\[\equiv\sim\mathrm{p}\lor\sim\mathrm{q}\]
