If A = {2, 4, 6, 8}, what are the total number of subsets and the number of two-element subsets, respectively?
Answer and explanation
Correct answer: 16 and 6
The set A has 4 elements. A set with n elements has 2^n total subsets because each element can either be included or excluded. Therefore, A has 2^4 = 16 subsets. The number of subsets containing exactly two elements is given by the combination 4C2 = 4!/(2!2!) = 6. Hence, the required numbers are 16 and 6, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
16 and 6
Why is this the correct answer?
The set A has 4 elements. A set with n elements has 2^n total subsets because each element can either be included or excluded. Therefore, A has 2^4 = 16 subsets. The number of subsets containing exactly two elements is given by the combination 4C2 = 4!/(2!2!) = 6. Hence, the required numbers are 16 and 6, 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.
