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Standard XI

Mathematics

Power Set

For a set X=2...

Question

For a set $X = {2, 3, {2, 3}}, P (X) =$

{{2}, {3}, {{2, 3}}}

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{\emptyset, {2}, {3}, {{2, 3}}}

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{\emptyset, {2}, {3}, {{2, 3}}, {2, {2, 3}}, {3, {2, 3}}}

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{\emptyset, {2}, {3}, {{2, 3}}, {2, {2, 3}}, {3, {2, 3}}, {2, 3, {2, 3}}}

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Solution

The correct option is C ${\emptyset, {2}, {3}, {{2, 3}}, {2, {2, 3}}, {3, {2, 3}}}$
Given set $X = {2, 3, {2, 3}}$
Now, to find power set of this set, first we must find all the subsets of $X .$
Now, the subsets of $X$ are given as: $\emptyset, {2}, {3}, {2, 3}, {2, {2, 3}}, {3, {2, 3}}, {2, 3 {2, 3}}$

Hence the power set of $X or,$
$P (X) = {\emptyset, {2}, {3}, {2, 3}, {2, {2, 3}}, {3, {2, 3}}, {2, 3, {2, 3}}}$

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For a set X={2,3,{2,3}},P(X)=

For a set $X = {2, 3, {2, 3}}, P (X) =$