If A = {x ∈ N : x ≤ 20}, B = {x : x is odd and x ≤ 20}, and C = {x : x is a multiple of 5 and x ≤ 20}, what is n(B ∩ C)?
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Answer and explanation
Correct answer: 2
The positive multiples of 5 not exceeding 20 are 5, 10, 15, and 20. Of these, 5 and 15 are odd, whereas 10 and 20 are even. Therefore B ∩ C = {5, 15}, and its cardinality is 2. Set A gives the common upper bound but is not needed for this particular intersection.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The positive multiples of 5 not exceeding 20 are 5, 10, 15, and 20. Of these, 5 and 15 are odd, whereas 10 and 20 are even. Therefore B ∩ C = {5, 15}, and its cardinality is 2. Set A gives the common upper bound but is not needed for this particular intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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