Lecture 2 : Relations

Let R be the relation on Zdefined by R = {(a, b): a, b ∈ Z, a - b is an integer}. Find the domain and range of R.

Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

 Write the relation R = {(x, x³): x is a prime number less than 10} in roster form.

Determine the domain and range of the relation R defined by R = {(x, x+ 5): x ∈{0, 1, 2, 3, 4, 5}}.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by

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

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

The given figure shows a relationship between the sets P and Q. write this relation

(i) in set-builder form (ii) in roster form.

What is its domain and range?

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between xand yis odd; x ∈A, y ∈B}. Write R in roster form.

Define a relation R on the set Nof natural numbers by R = {(x, y): y= x+ 5, xis a natural number less than 4; x,y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.

Let A = {1, 2, 3, ... , 14}. Define a relation R from A to A by R = {(x, y): 3x - y = 0, where x, y ∈ A}. Write down its domain, codomain and range.