Question

1. A - 11.3), then write the identity relation 1 : AA. Also write the
universal relation on A.
2. IA 1.2) then write down all the relations on A.
3. IfA - {1, 2, 3}then find the elements of the relation R - {y)
{6.: -
y and x, yeA) on A.
4. Z is the set of positive integers and R: Z →is a relation defined
as R = {(a,b) | a,bez and a - b>2). Is it a finite relation? Represent R
as a set in the Roster Form.
5. A = {2,3,4,5) and B = {3,6,7,10) be two sets and a relation R is defined
as R = {(x,y) : x completely divides y where xe A and yeB). Write the
relation R in the Tabular form. Also represent R by arrow diagram and
matrix table.
Determine R-' of the relation R given in Question 5 above. Also find
d(R-!) and r(R-!).
7. A = {3,6,8,9} is a set and aRb iff a-b is divisible by 3 for a be A. Then
(i) Write R as a set and draw the arrow diagram.
(ii) Find d(R) and r(R).
(iii) Can we find the inverse of R?
8. A = {1,2,3,4} and B {a,b,c,d) be two sets. Choose which of the
followings are relations from A to B-
(i) {(1,a), (1,5), (2,C), (4,d)} (ii) {(1,1), (1,2), (3.c)}
(iii) AXB
(iv) {(a,1), (6,2), (0,3)}
(v) {0}
(vi) {(1,c), (2,6), (3.c), (4,0)}
9. A relation R is defined on the set of natural numbers N as aRb where
a=b2 for a,ben. Write the relation R. Also write R'in set builder
method.
10. If A = {1,2,3,4,6} and R is a relation on A defined as R = {(x,y): y is
exactly divisible be r where x, yeA) then
(i) How many elements are there in R and list them?
(ii) find R-1
(iii) find d(R), (R), d(R) and r(R')​

Answer 1

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10. If A = {1,2,3,4,6} and R is a relation on A defined as R = {(x,y): y is exactly divisible be r where x, yeA) then

• (i) How many elements are there in R and list them?
• (ii) find R-1
• (iii) find d(R), (R), d(R) and r(R')

Answer::-

A={1,2,3,4,6}

R={(a,b):a,b∈A,b is exactly divisible by a}

• (i) 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)}
• (ii) Domain of R={1,2,3,4,6}
• (iii) Range of R={1,2,3,4,6}