If A = {1, 2, 3, 4}, how many subsets contain 1 and 2 together or contain neither 1 nor 2?
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Answer and explanation
Correct answer: 8
There are two mutually exclusive cases. In the first, both 1 and 2 are included; elements 3 and 4 are free, giving 2² = 4 subsets. In the second, both 1 and 2 are excluded; again 3 and 4 are free, giving 2² = 4 subsets. Adding the disjoint cases gives 4 + 4 = 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
There are two mutually exclusive cases. In the first, both 1 and 2 are included; elements 3 and 4 are free, giving 2² = 4 subsets. In the second, both 1 and 2 are excluded; again 3 and 4 are free, giving 2² = 4 subsets. Adding the disjoint cases gives 4 + 4 = 8.
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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