Let 1 2 2 3 3 4 and 1 1 1 2 2 1 2 2 2 3 3 1 3 2 3 3 3 4 be

Let = {(1, 2), (2, 3), (3, 4)} and = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Then find the indicated relations.

a) Find the union of the given relations R1 and R2. is _____.

b) Find the intersection of the given relations R1 and R2. is _____.

c) Find the difference of the given relation R2 from R1. is _____.

d) Find the difference of the given relation R1 from R2. is _____. (

Write the ordered pairs (a,b) in increasing order of first a and then b, separated by commas with one space after commas. For example, (1, 2), (1, 4), (2, 3), (3, 4), (3, 5). Remember to use proper set notation when entering the relations.) (Please enter \"null\" if the relations consist of no ordered pairs.)

Solution

a)

Union of the given relations R1 and R2 will contain all the ordered pair present in either R1 and R2 but no ordered will be repeated

therefore

{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

b)

intersection of the given relations R1 and R2 contain all the ordered pair wich is common in both R1 and R2

therefore

{(1, 2), (2, 3), (3, 4)}

c)

difference of the given relation R2 from R1 (R2 - R1)

it will show all the ordered pair which are present in R2 but not in R1

therefore

{(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}

d)

difference of the given relation R1 from R2 (R1 - R2)

it will show all the ordered pair which are present in R1 but not in R2

therefore

{null}