If \(A=\{1,2,3,4\}\), how many subsets contain 1 or 2?
Answer and explanation
Correct answer: 12
The set \(A\) has four elements, so it has \(2^4=16\) total subsets. It is easier to count the complement: subsets containing neither 1 nor 2 can use only the elements 3 and 4, giving \(2^2=4\) subsets. Hence the number containing 1 or 2 is \(16-4=12\). Here “or” is inclusive, so subsets containing both 1 and 2 are also counted. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The set \(A\) has four elements, so it has \(2^4=16\) total subsets. It is easier to count the complement: subsets containing neither 1 nor 2 can use only the elements 3 and 4, giving \(2^2=4\) subsets. Hence the number containing 1 or 2 is \(16-4=12\). Here “or” is inclusive, so subsets containing both 1 and 2 are also counted. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
