If U = {1,2,3,4,5,6,7,8,9,10,11,12} and A = {x ∈ U : x is a multiple of 3}, what is Aᶜ?
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Answer and explanation
Correct answer: {1,2,4,5,7,8,10,11}
The multiples of 3 that lie in U are 3, 6, 9, and 12, so A = {3,6,9,12}. The complement contains every element of U that is not a multiple of 3. Removing these four multiples from U gives Aᶜ = {1,2,4,5,7,8,10,11}. Thus option B is correct; options A and D list only multiples of 3.
Frequently asked questions
What is the correct answer to this question?
{1,2,4,5,7,8,10,11}
Why is this the correct answer?
The multiples of 3 that lie in U are 3, 6, 9, and 12, so A = {3,6,9,12}. The complement contains every element of U that is not a multiple of 3. Removing these four multiples from U gives Aᶜ = {1,2,4,5,7,8,10,11}. Thus option B is correct; options A and D list only multiples of 3.
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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