If the universal set is U = {1, 2, 3, ..., 15} and A = {x ∈ U : x is odd}, what is the value of Aᶜ ∩ {x ∈ U : 3 divides x}?
Answer and explanation
Correct answer: {6, 12}
Since A is the set of odd numbers in U, its complement Aᶜ is the set of even numbers: {2, 4, 6, 8, 10, 12, 14}. The other set contains multiples of 3 in U: {3, 6, 9, 12, 15}. An intersection keeps only elements common to both sets. The common elements are 6 and 12, so Aᶜ ∩ {multiples of 3} = {6, 12}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{6, 12}
Why is this the correct answer?
Since A is the set of odd numbers in U, its complement Aᶜ is the set of even numbers: {2, 4, 6, 8, 10, 12, 14}. The other set contains multiples of 3 in U: {3, 6, 9, 12, 15}. An intersection keeps only elements common to both sets. The common elements are 6 and 12, so Aᶜ ∩ {multiples of 3} = {6, 12}. Therefore, 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.
