If A = {1, 4, 9, 16} and B = {1, 2, 4, 8, 16}, which of the following is A ∩ B?
Answer and explanation
Correct answer: {1, 4, 16}
The governing concept is set intersection. The intersection A∩B contains exactly those elements that occur in both A and B, not elements that occur in only one set. Compare the members of A={1,4,9,16} with B={1,2,4,8,16}. The number 1 appears in both, 4 appears in both, and 16 appears in both. The number 9 occurs only in A, while 2 and 8 occur only in B. Therefore A∩B={1,4,16}, so option A is correct. Option B incorrectly selects the element unique to A. Option C lists elements unique to B. Option D contains every element from either set, so it represents the union A∪B rather than the intersection. Repeated elements are written only once in a set.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 16}
Why is this the correct answer?
The governing concept is set intersection. The intersection A∩B contains exactly those elements that occur in both A and B, not elements that occur in only one set. Compare the members of A={1,4,9,16} with B={1,2,4,8,16}. The number 1 appears in both, 4 appears in both, and 16 appears in both. The number 9 occurs only in A, while 2 and 8 occur only in B. Therefore A∩B={1,4,16}, so option A is correct. Option B incorrectly selects the element unique to A. Option C lists elements unique to B. Option D contains every element from either set, so it represents the union A∪B rather than the intersection. Repeated elements are written only once in a set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
