Discussion
Let A be the set of odd integers in [0,10] and let B be the set of prime numbers in [0,10]. If \(R = \{(a, b) \in A \times B : a + b \text{ is odd}\}\), then n(R)=
Answer: E
n(R) = 5.
A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}. Since every a in A is odd, a + b is odd only when b is even, and the only even prime is 2.
So R = {(1,2), (3,2), (5,2), (7,2), (9,2)}, which has 5 elements.
Pairing an odd a with an odd prime (3, 5 or 7) gives an even sum, so those pairs are excluded. Counting only the odd primes, or only some of the five odd numbers, leads to the smaller options.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development