How many proper subsets does a set with two elements have?
Answer and explanation
Correct answer: 3
A set containing n elements has 2^n subsets because each element can either be included or excluded. For n = 2, the total number of subsets is 2^2 = 4. These are the empty set, the two one-element subsets, and the original set. A proper subset is any subset other than the set itself, so the number of proper subsets is 4 - 1 = 3. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
A set containing n elements has 2^n subsets because each element can either be included or excluded. For n = 2, the total number of subsets is 2^2 = 4. These are the empty set, the two one-element subsets, and the original set. A proper subset is any subset other than the set itself, so the number of proper subsets is 4 - 1 = 3. Therefore, 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.
