If A={a,b,c}, how many subsets in P(A) have an odd number of elements?
Answer and explanation
Correct answer: 4
For a three-element set, an odd-sized subset has either one element or three elements. There are C(3,1)=3 one-element subsets: {a}, {b}, and {c}. There is C(3,3)=1 three-element subset, namely {a,b,c}. Thus the total number is 3+1=4, so option A is correct. The empty set and two-element subsets have even size and are excluded.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a three-element set, an odd-sized subset has either one element or three elements. There are C(3,1)=3 one-element subsets: {a}, {b}, and {c}. There is C(3,3)=1 three-element subset, namely {a,b,c}. Thus the total number is 3+1=4, so option A is correct. The empty set and two-element subsets have even size and are excluded.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
