Q7.Marks: +2.0UGC NET Paper 2: Computer Science17th June 2023
Let R = {x : x ∈ N, x is multiple of 3 and x ≤ 100} and S = {x : x ∈ N, x is a multiple of 5 and x < 100}. What is the number of elements in (R ∩ S) × (S ∩ R)?
1.36✓ Correct
2.33
3.20
4.6
Solution
The correct answer 36
Key Points
The set R is the set of natural numbers less than or equal to 100 that are multiples of 3, while the set S is the set of natural numbers less than 100 that are multiples of 5.
The intersection of these two sets, R ∩ S, would be multiples of both 3 and 5, or multiples of 15, that are less than 100. The multiples of 15 that are less than or equal to 100 are {15, 30, 45, 60, 75, 90}, so there are 6 elements in the intersection of these sets.
The cartesian product (R ∩ S) × (S ∩ R) would involve all ordered pairs where the first element is chosen from R ∩ S and the second element is chosen from S ∩ R. However, since the sets R ∩ S and S ∩ R are the same, this is basically choosing two elements from the set R ∩ S, which has 6 elements.
