Question:
If
\[
A = \{ x / x \text{ is a prime number}, 0 \leq x \leq 9 \}, \text{ then the number of elements of the power set of } A \text{ is}
\]
If
\[
A = \{ x / x \text{ is a prime number}, 0 \leq x \leq 9 \}, \text{ then the number of elements of the power set of } A \text{ is}
\]
Show Hint
The number of elements in the power set of a set with \( n \) elements is \( 2^n \).
Updated On: Jan 30, 2026
- 12
- 4
- 16
- 8
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The Correct Option is C
Solution and Explanation
Step 1: Find the elements of set A.
The prime numbers between 0 and 9 are \( \{2, 3, 5, 7\} \). Therefore, set \( A = \{2, 3, 5, 7\} \).
Step 2: Calculate the number of elements in the power set.
The number of elements in the power set of a set with \( n \) elements is \( 2^n \). Since the set \( A \) has 4 elements, the power set has \( 2^4 = 16 \) elements.
Step 3: Conclusion.
Thus, the number of elements in the power set of \( A \) is 16, corresponding to option (C).
The prime numbers between 0 and 9 are \( \{2, 3, 5, 7\} \). Therefore, set \( A = \{2, 3, 5, 7\} \).
Step 2: Calculate the number of elements in the power set.
The number of elements in the power set of a set with \( n \) elements is \( 2^n \). Since the set \( A \) has 4 elements, the power set has \( 2^4 = 16 \) elements.
Step 3: Conclusion.
Thus, the number of elements in the power set of \( A \) is 16, corresponding to option (C).
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