If U = {1, 2, ..., 50} and A = {x : x ∈ U, the last digit of x is 2 or 7}, what is n(A′)?
Answer and explanation
Correct answer: 40
List the numbers from 1 to 50 whose last digit is 2 or 7: 2, 7, 12, 17, 22, 27, 32, 37, 42, and 47. Thus n(A) = 10. The universal set U has 50 elements, and the complement-count formula is n(A′) = n(U) − n(A). Therefore n(A′) = 50 − 10 = 40. Option A is correct. Option B counts A itself, while options C and D result from incorrect counting of the qualifying last digits.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
List the numbers from 1 to 50 whose last digit is 2 or 7: 2, 7, 12, 17, 22, 27, 32, 37, 42, and 47. Thus n(A) = 10. The universal set U has 50 elements, and the complement-count formula is n(A′) = n(U) − n(A). Therefore n(A′) = 50 − 10 = 40. Option A is correct. Option B counts A itself, while options C and D result from incorrect counting of the qualifying last digits.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
