If U = {1, 2, ..., 36}, A = {x ∈ U : x is divisible by 2}, B = {x ∈ U : x is divisible by 3}, and C = {x ∈ U : x is divisible by 6}, what is |(A ∪ B ∪ C)'|?
Answer and explanation
Correct answer: 12
Every multiple of 6 is already a multiple of both 2 and 3, so C is contained in A ∩ B and does not add any new element to the union. In U there are 18 multiples of 2 and 12 multiples of 3; 6 numbers are multiples of both. Therefore |A ∪ B| = 18 + 12 − 6 = 24. The complement has 36 − 24 = 12 elements, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Every multiple of 6 is already a multiple of both 2 and 3, so C is contained in A ∩ B and does not add any new element to the union. In U there are 18 multiples of 2 and 12 multiples of 3; 6 numbers are multiples of both. Therefore |A ∪ B| = 18 + 12 − 6 = 24. The complement has 36 − 24 = 12 elements, so option C 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.
