If A={r,s,t,u,v}, how many elements of P(A) are supersets of {r,s} but do not contain v?
Answer and explanation
Correct answer: 4
Any required subset must contain r and s, because it must be a superset of {r,s}. The element v is forbidden. The remaining elements t and u may each be selected or not selected independently. Thus there are 2 choices for t and 2 choices for u, giving 2×2=2^2=4 valid subsets: {r,s}, {r,s,t}, {r,s,u}, and {r,s,t,u}. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Any required subset must contain r and s, because it must be a superset of {r,s}. The element v is forbidden. The remaining elements t and u may each be selected or not selected independently. Thus there are 2 choices for t and 2 choices for u, giving 2×2=2^2=4 valid subsets: {r,s}, {r,s,t}, {r,s,u}, and {r,s,t,u}. Therefore, 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.
