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What does the shaded region represent in the figure given below
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Verified Answer
The correct answer is:
$(\mathrm{P} \cap \mathrm{Q}) \cup(\mathrm{P} \cap \mathrm{R})$
The shaded region represents $(\mathrm{P} \cap \mathrm{Q}) \cup(\mathrm{P} \cap \mathrm{R})$ Let the intersecting sets $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ divide it into $7 \mathrm{regions}$ marked, a to g as shown below.
The shaded part contains regions $\mathrm{b}, \mathrm{c}$, and $\mathrm{d}$.
(a) $(\mathrm{P} \cup \mathrm{Q})-(\mathrm{P} \cap \mathrm{Q})=$ regions $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{f}, \mathrm{g},-\mathrm{b}, \mathrm{c}$
$=\mathrm{a}, \mathrm{d}, \mathrm{f}_{\mathrm{g}} \mathrm{g}$, notcorrect.
(b) $(\mathrm{P} \cap(\mathrm{Q} \cap \mathrm{R})=\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \cap \mathrm{c}, \mathrm{f}=\mathrm{c}$ not correct.
(c) $(P \cap Q) \cap(P \cap R)=$ regions $b, c, \cap r e g i o n, c, d=c, s o$
not correct
(d) $(P \cap Q) \cup(P \cap R)=$ regions $b, c, \cup c, d=b, c, d s o$
correct
The shaded part contains regions $\mathrm{b}, \mathrm{c}$, and $\mathrm{d}$.
(a) $(\mathrm{P} \cup \mathrm{Q})-(\mathrm{P} \cap \mathrm{Q})=$ regions $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{f}, \mathrm{g},-\mathrm{b}, \mathrm{c}$
$=\mathrm{a}, \mathrm{d}, \mathrm{f}_{\mathrm{g}} \mathrm{g}$, notcorrect.
(b) $(\mathrm{P} \cap(\mathrm{Q} \cap \mathrm{R})=\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \cap \mathrm{c}, \mathrm{f}=\mathrm{c}$ not correct.
(c) $(P \cap Q) \cap(P \cap R)=$ regions $b, c, \cap r e g i o n, c, d=c, s o$
not correct
(d) $(P \cap Q) \cup(P \cap R)=$ regions $b, c, \cup c, d=b, c, d s o$
correct
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