If U = {1, 2, ..., 16}, A = {x ∈ U : x is a square number}, and B = {x ∈ U : x is odd}, what is A′ ∩ B?
Answer and explanation
Correct answer: {3, 5, 7, 11, 13, 15}
The odd elements of U are B = {1, 3, 5, 7, 9, 11, 13, 15}. The square numbers in U are {1, 4, 9, 16}; among these, the odd square numbers are 1 and 9. A′ contains numbers that are not squares, so intersecting A′ with B removes 1 and 9 from the odd set. The result is {3, 5, 7, 11, 13, 15}, which is option A.
Frequently asked questions
What is the correct answer to this question?
{3, 5, 7, 11, 13, 15}
Why is this the correct answer?
The odd elements of U are B = {1, 3, 5, 7, 9, 11, 13, 15}. The square numbers in U are {1, 4, 9, 16}; among these, the odd square numbers are 1 and 9. A′ contains numbers that are not squares, so intersecting A′ with B removes 1 and 9 from the odd set. The result is {3, 5, 7, 11, 13, 15}, which is option A.
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.
