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What is the Cardinality of the Power set of the set $\{0,1,2\}$?

1. $8$
2. $6$
3. $7$
4. $9$

### 1 comment

Option A is correct.

The cardinality of any set is the size of the set or the total number of elements present in the set.

For a given set $A$ Power set of $A$ is set of all the subsets of set $A$

Let $P=\left\{0,1,2\right\}\implies P(A)=\left\{\phi,\left\{0\right\},\left\{1\right\},\left\{2\right\},\left\{0,1\right\},\left\{0,2\right\},\left\{1,2\right\},\left\{0,1,2\right\}\right\}$

So cardinality of $P(A)\implies 8$ elements
cardinality of power set = { phi, {0}, {1}, {2},  {0,1} , {1,2}, {0,2} , { 0,1,2}}

Option A is correct.
8, cardinality of power set = 2^n so if n =3 then 2^3=8

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