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Standard XII

Mathematics

Power Set of a 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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Similar questions

Q. For a set

X = {2, 3, {2, 3}}, P (X) =

Q. For a non-empty set

X

, if operation

* : P (X) \times P (X) \Rightarrow P (X)

is defined as

A * B = (A - B) \cup (B - A), \forall A, B \in P (X)

then show that empty set

ϕ

is the identity for

*,

and all elements

A

P (X)

are invertible with

A^{- 1} = A

Given non-empty set X, consider the binary operation $* : P (X) \times P (X) \to P (X)$ given by $A * B = A \cap B \forall A, B$ in P(X), where P(X)is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation.

Q. Given a non-empty set

X

, consider the binary operation

* : P (X) \times P (X) \to P (X)

given by

A * B = A \cap B \forall A, B

P (X)

, where

P (X)

is the power set of

X

. Show that

X

is the identity element for this operation and

X

is the only invertible element in

P (X)

with respect to the operation

*

Given a non-empty set X, consider the binary operation *: P(X) × P(X) → P(X) given by A * B = A ∩ B &mnForE; A, B in P(X) is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation*.

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

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