10. If A={1,2,3,4,6} and R is a relation on A defined as R={(x,y):y is exactly divisible by x where x,yЄA} then - Advance Math Class 10 - Exercise 1.3
Related Quarries: relation r in the set a= 1 2 3 4 5 6 as r= (x y) y is divisible by x, let a = 1 2 3 4 6 let r be the relation on a defined by, let a = 1 2 3 4 5 6 let r be the relation on a defined by, let a 1 2 3 14 define a relation r from a to a by r= (x y) 3x-y=0, let a = 2 3 4 5 6 let r be the relation on a defined by, determine the domain and range of the relation r defined by, if r is a relation from a to b, then the domain of r is, let a = (1, 2, 3, 4, 5) and r be a relation from a to a r = ((x,y): y = x + 1 find the range).
Solution:
Given
A = {1, 2, 3, 4, 6}
i. How many elements are there in R and list them?
Answer:
R = {(1, 1), (1, 2),(1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}
There are 12 elements in R.
ii. Find ?
Answer: = {(1, 1), (2, 1),(3, 1), (4, 1), (6, 1), (2, 2), (4, 2), (6, 2),
(3, 3), (6, 3), (4, 4), (6, 6)}
iii. Find d(R), r(R), and
?
Answer:
d(R) = {1, 2, 3, 4, 6}
r(R) = {1, 2, 3, 4, 6}
= {1, 2, 3, 4, 6}
= {1, 2, 3, 4, 6}
Exercise: 1.3
1. If A = {1, 3}, then write the identity relation I : A⟶A. Also write the universal relation on A ?
2. If A = {1, 2} then write down all the relation on A ?
3. If A = (1, 2, 3) then find the elements of the relation R= {(x, y): x=y and x, y Є A} on A ?
6. Determine R^-1 of the relation R given in question 5 above. Also find d(R^-1) and r(R^-1) ?