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Joint Entrance Examination
Mathematics
Mathematical Reasoning
Question 87
Question 87 of 103
Medium
MCQ
The converse of \[((\sim p) \wedge q) \Rightarrow r\] is
A
\[((\sim p) \vee q) \Rightarrow r\]
B
\[(\sim \mathrm{r}) \Rightarrow \mathrm{p} \wedge \mathrm{q}\]
C
\[(\mathrm{p} \vee(\sim \mathrm{q})) \Rightarrow(\sim \mathrm{r})\]
D
\[(\sim \mathrm{r}) \Rightarrow((\sim \mathrm{p}) \wedge \mathrm{q})\]
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Official solution
Converse of
(
(
∼
p
)
∧
q
)
⇒
r
((\sim p) \wedge q) \Rightarrow r
((
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)
∧
q
)
⇒
r
\[
≡
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⇒
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∧
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≡
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r
∨
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∧
q
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≡
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∨
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≡
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r
\begin{aligned} & \equiv \mathrm{r} \Rightarrow(\sim \mathrm{p} \wedge \mathrm{q}) \\\\ & \equiv \sim \mathrm{r} \vee(\sim \mathrm{p} \wedge \mathrm{q}) \\\\ & \equiv \sim \mathrm{r} \vee(\mathrm{p} \vee \sim \mathrm{q}) \equiv(\mathrm{p} \vee \sim \mathrm{q}) \Rightarrow \sim \mathrm{r} \end{aligned}
≡
r
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∧
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≡∼
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∨
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∧
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≡∼
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∨
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∨
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q
)
≡
(
p
∨
∼
q
)
⇒∼
r
\]
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