For Y = {x ∈ N : x ≤ 30 and x is divisible by neither 2 nor 3}, which elements from 1 to 10 belong to Y?
Answer and explanation
Correct answer: {1, 5, 7}
Examine the integers 1 through 10. The numbers divisible by 2 are 2, 4, 6, 8, and 10; the numbers divisible by 3 are 3, 6, and 9. Since the phrase “neither 2 nor 3” excludes every number in either group, remove their union. The numbers left are 1, 5, and 7. Hence the required members are {1, 5, 7}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
{1, 5, 7}
Why is this the correct answer?
Examine the integers 1 through 10. The numbers divisible by 2 are 2, 4, 6, 8, and 10; the numbers divisible by 3 are 3, 6, and 9. Since the phrase “neither 2 nor 3” excludes every number in either group, remove their union. The numbers left are 1, 5, and 7. Hence the required members are {1, 5, 7}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
