RD Chapter 2 Relations Ex 2.3 Solutions
Question - 11 : - Let A = {a, b}. List all relations on A and find their number.
Answer - 11 : -
The total number of relations that can be defined from a set A to a set B is the number of possible subsets of A × B. If n (A) = p and n (B) = q, then n (A × B) = pq.
So, the total number of relations is 2pq.
Now,
A × A = {(a, a), (a, b), (b, a), (b, b)}
Total number of relations are all possible subsets of A × A:
[{(a, a), (a, b), (b, a), (b, b)}, {(a, a), (a, b)}, {(a, a), (b, a)},{(a, a), (b, b)}, {(a, b), (b, a)}, {(a, b), (b, b)}, {(b, a), (b, b)}, {(a, a), (a, b), (b, a)}, {(a, b), (b, a), (b, b)}, {(a, a), (b, a), (b, b)}, {(a, a), (a, b), (b, b)}, {(a, a), (a, b), (b, a), (b, b)}]
n (A) = 2 ⇒ n (A × A) = 2 × 2 = 4
∴ Total number of relations = 24 = 16
Question - 12 : - 
Answer - 12 : -
Question - 13 : - 
Answer - 13 : -
Question - 14 : -
Answer - 14 : -
Question - 15 : - 
Answer - 15 : -
Question - 16 : - Let f be a realfunction given by 
Find each of thefollowing
- fof
- fofof
- (f0f0f) (38)
- f2Also, show that fof ≠ f2 .
Answer - 16 : - 1.
2.
3.
4.
Question - 17 : - 
Answer - 17 : -