If A = {0, 2, 4, 6}, how many elements does P(A) have?
Answer and explanation
Correct answer: 16
The set A contains four distinct elements: 0, 2, 4, and 6. For a finite set with n elements, every element has two independent possibilities in a subset: it is either included or excluded. Consequently, the power set has 2ⁿ subsets. Here n = 4, so |P(A)| = 2⁴ = 16. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The set A contains four distinct elements: 0, 2, 4, and 6. For a finite set with n elements, every element has two independent possibilities in a subset: it is either included or excluded. Consequently, the power set has 2ⁿ subsets. Here n = 4, so |P(A)| = 2⁴ = 16. Therefore, option C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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