If U = {1, 2, ..., 70}, A = {x ∈ U : 2 divides x}, and B = {x ∈ U : 7 divides x}, what is n((A − B)′)?
Answer and explanation
Correct answer: 40
A contains the 35 even numbers from 1 to 70. The set A − B contains even numbers that are not divisible by 7. An even number divisible by 7 must be divisible by 14; the multiples of 14 in U are 14, 28, 42, 56, and 70, so there are 5 such numbers. Therefore n(A − B) = 35 − 5 = 30. Its complement in a 70-element universal set has 70 − 30 = 40 elements. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
A contains the 35 even numbers from 1 to 70. The set A − B contains even numbers that are not divisible by 7. An even number divisible by 7 must be divisible by 14; the multiples of 14 in U are 14, 28, 42, 56, and 70, so there are 5 such numbers. Therefore n(A − B) = 35 − 5 = 30. Its complement in a 70-element universal set has 70 − 30 = 40 elements. Option A is correct.
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.
