If A = {p, q, r, s, t}, how many subsets of A do not contain p?
Answer and explanation
Correct answer: 16
To form a subset that does not contain p, p is excluded permanently. The remaining four elements q, r, s, and t are each free to be included or excluded independently. Therefore the number of valid subsets is 2⁴ = 16. Another way to see this is that all subsets of the four-element set {q, r, s, t} are exactly the subsets of A that omit p. The empty subset is included in this count.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
To form a subset that does not contain p, p is excluded permanently. The remaining four elements q, r, s, and t are each free to be included or excluded independently. Therefore the number of valid subsets is 2⁴ = 16. Another way to see this is that all subsets of the four-element set {q, r, s, t} are exactly the subsets of A that omit p. The empty subset is included in this count.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
