If A={1,2,3,4}, how many elements of P(A) do not contain 1 and do contain 4?
Answer and explanation
Correct answer: 4
We are counting subsets of A in which 1 is definitely excluded and 4 is definitely included. Therefore only 2 and 3 remain free: each may be included or excluded independently. The number of choices is 2×2=2^2=4. The four subsets are {4}, {2,4}, {3,4}, and {2,3,4}. Thus option C is correct; treating 1 or 4 as free would overcount the possibilities.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
We are counting subsets of A in which 1 is definitely excluded and 4 is definitely included. Therefore only 2 and 3 remain free: each may be included or excluded independently. The number of choices is 2×2=2^2=4. The four subsets are {4}, {2,4}, {3,4}, and {2,3,4}. Thus option C is correct; treating 1 or 4 as free would overcount the possibilities.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
