If A = {1,2,3,4} and B = {3,4,5,6}, what is |P(A ∪ B)| − |P(A ∩ B)|?
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Answer and explanation
Correct answer: 60
The union is A ∪ B = {1,2,3,4,5,6}, so it has 6 elements and its power set has 2^6 = 64 elements. The intersection is A ∩ B = {3,4}, so it has 2 elements and its power set has 2^2 = 4 elements. Hence the required difference is 64 − 4 = 60, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
The union is A ∪ B = {1,2,3,4,5,6}, so it has 6 elements and its power set has 2^6 = 64 elements. The intersection is A ∩ B = {3,4}, so it has 2 elements and its power set has 2^2 = 4 elements. Hence the required difference is 64 − 4 = 60, so option C 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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