If U = {x ∈ N : 1 ≤ x ≤ 12} and A = {x : x is divisible by both 2 and 3}, what is Aᶜ?
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Answer and explanation
Correct answer: {1,2,3,4,5,7,8,9,10,11}
A number divisible by both 2 and 3 must be divisible by their least common multiple, 6. Within U = {1,2,...,12}, the numbers divisible by 6 are 6 and 12, so A = {6,12}. The complement contains every other element of U: {1,2,3,4,5,7,8,9,10,11}. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,4,5,7,8,9,10,11}
Why is this the correct answer?
A number divisible by both 2 and 3 must be divisible by their least common multiple, 6. Within U = {1,2,...,12}, the numbers divisible by 6 are 6 and 12, so A = {6,12}. The complement contains every other element of U: {1,2,3,4,5,7,8,9,10,11}. Hence 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.
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