If \(A=\{1,2,3,4\}\), how many subsets can be formed that contain only even elements?
Answer and explanation
Correct answer: 4
The even elements of \(A\) are 2 and 4, so the relevant set is \(\{2,4\}\), which has two elements. Each element can either be included or excluded independently when forming a subset. Hence the number of subsets is \(2^2=4\): \(\emptyset\), \(\{2\}\), \(\{4\}\), and \(\{2,4\}\). The empty set is included because it contains no odd elements and is a valid subset.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The even elements of \(A\) are 2 and 4, so the relevant set is \(\{2,4\}\), which has two elements. Each element can either be included or excluded independently when forming a subset. Hence the number of subsets is \(2^2=4\): \(\emptyset\), \(\{2\}\), \(\{4\}\), and \(\{2,4\}\). The empty set is included because it contains no odd elements and is a valid subset.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
