A={2,3}, B={1,3,5} , then the number of relations from A to B is (i) 2 (ii) 64 (iii) 32 (iv) 62 (b) R is a relation defined on the set A = {1,2,3, … . , 14} by R = {(x, y): 3 − y = 0, x, y ∈ A}. Write the domain and range of R
Answers
Answer:
ii) 64
Step-by-step explanation:
hope it will help you
Given
- A={2,3}
- B={1,3,5}
(b) the correct question for the B part of the question would be, the relation given by R = {(x, y): 3x − y = 0, x, y ∈ A}.
- A = {1,2,3, … . , 14}
- R = {(x, y): 3x − y = 0, x, y ∈ A}.
To find
- number of relations from A to B
- the domain and range of R
Solution
we are provided to sets namely A and B and are asked to find the number of relations that exist between them.
the standard equation to find the number of relations is given by 2^(pq) where p and q are the elements of the set A and B respectively
number of elements of the first set = 2
number of elements in second set = 3
number of relations = 2^(2×3) = 2^6
or, 64
(b) 3x - y= 0
latest substitute the value of x from the elements of the first set. it must be noted that the value obtained for why should also belong to the set A
3×1 - y = 0
or , y = 3
in a similar manner we can get all the values of y as,
3, 6,9,12. for the values of x, 1,2,3,4 respectively.
R = {(1,3),(2,6),(3,9),(4,12)}
the domain of the relation would be,
domain of the relation would be,D ={1,2,3,4}
domain of the relation would be,D ={1,2,3,4}range would be = {3,6,9,12}