If n(A) = 59 and n(A ∩ B) = 24, how many elements are only in A, that is, in A but not in B?
Answer and explanation
Correct answer: 35
The total n(A) consists of the elements only in A together with the elements in the overlap A ∩ B. Therefore, n(A only) = n(A) − n(A ∩ B) = 59 − 24 = 35. The value 24 represents the common region, while 59 represents all elements of A, including that common region. Thus option B is correct; 83 does not follow from the given cardinalities.
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
The total n(A) consists of the elements only in A together with the elements in the overlap A ∩ B. Therefore, n(A only) = n(A) − n(A ∩ B) = 59 − 24 = 35. The value 24 represents the common region, while 59 represents all elements of A, including that common region. Thus option B is correct; 83 does not follow from the given cardinalities.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
