NIMCET 2020 — Mathematics PYQ

1. Understand the Definitions:

• Set: A collection of distinct objects. Here, set $A=\{x,y,z\}$.

• Power Set: The power set of a set $A$, denoted as $P(A)$, is the set of all possible subsets of $A$.

• The question asks for the total number of elements (subsets) contained within the power set of $A$.

2. Find the Number of Elements in Set $A$:

Count the elements present inside the given set $A$:

$$\text{Number of elements }(n)=3$$

3. Apply the Formula:

The total number of subsets of a set containing $n$ elements (which equals the number of elements in its power set) is given by the formula:

$$\text{Number of subsets}=2^n$$

Substituting the value of $n=3$:

$$\text{Number of subsets}=2^3$$

$$\text{Number of subsets}=2\times 2\times 2=8$$

4. Verification (Listing the Subsets):

The actual subsets that make up the power set $P(A)$ are:

$$P(A)=\{\varnothing ,\{x\},\{y\},\{z\},\{x,y\},\{y,z\},\{x,z\},\{x,y,z\}\}$$

Counting them confirms there are exactly $8$ subsets.

Conclusion

The total number of elements inside the power set is 8.

Therefore, the correct option is B) 8.