If U = {1, 2, ..., 30} and A = {x : x is divisible by 2 or 3}, how many elements are in A'?
Answer and explanation
Correct answer: 10
Use inclusion–exclusion because numbers divisible by both 2 and 3 are counted in both groups. There are 30/2 = 15 multiples of 2 and 30/3 = 10 multiples of 3. Their common multiples are multiples of 6, numbering 30/6 = 5. Hence |A| = 15 + 10 − 5 = 20, and |A'| = 30 − 20 = 10. Therefore option C is correct; adding 15 and 10 without subtracting the overlap would give the wrong count.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Use inclusion–exclusion because numbers divisible by both 2 and 3 are counted in both groups. There are 30/2 = 15 multiples of 2 and 30/3 = 10 multiples of 3. Their common multiples are multiples of 6, numbering 30/6 = 5. Hence |A| = 15 + 10 − 5 = 20, and |A'| = 30 − 20 = 10. Therefore option C is correct; adding 15 and 10 without subtracting the overlap would give the wrong count.
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.
