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The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)' You are to examine these two statements carefully and select the answer. Assertion (A) : If P (A) $=\frac{3}{4}$ and $P(B)=\frac{3}{8}$, then $\mathrm{P}(\mathrm{A} \cup \mathrm{B}) \geq \frac{3}{4}$
Reason $(\mathrm{R}): \mathrm{P}(\mathrm{A}) \leq \mathrm{P}(\mathrm{A} \cup \mathrm{B})$ and $\mathrm{P}(\mathrm{B}) \leq \mathrm{P}(\mathrm{A} \cup \mathrm{B})$; hence
$\mathrm{P}(\mathrm{A} \cup \mathrm{B}) \geq \max .\{\mathrm{P}(\mathrm{A}), \mathrm{P}(\mathrm{B})\}$
Options:
Reason $(\mathrm{R}): \mathrm{P}(\mathrm{A}) \leq \mathrm{P}(\mathrm{A} \cup \mathrm{B})$ and $\mathrm{P}(\mathrm{B}) \leq \mathrm{P}(\mathrm{A} \cup \mathrm{B})$; hence
$\mathrm{P}(\mathrm{A} \cup \mathrm{B}) \geq \max .\{\mathrm{P}(\mathrm{A}), \mathrm{P}(\mathrm{B})\}$
Solution:
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Verified Answer
The correct answer is:
Both $\mathrm{A}$ and $\mathrm{R}$ are individually true but $\mathrm{R}$ is not the correct explanation of $\mathbf{A}$
A and R true but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$.
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