If A = {1,2,3} and B = {3,4}, how many elements does P(A ∪ B) have?
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Answer and explanation
Correct answer: 16
The union contains each distinct element from A and B only once. Thus A ∪ B = {1,2,3,4}, which has four elements; the repeated element 3 is counted only once. A set with four elements has 2⁴ subsets. Therefore P(A ∪ B) contains 16 elements, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The union contains each distinct element from A and B only once. Thus A ∪ B = {1,2,3,4}, which has four elements; the repeated element 3 is counted only once. A set with four elements has 2⁴ subsets. Therefore P(A ∪ B) contains 16 elements, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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