| |
|
|
| |
 |
| Relation |
|
| Consider the following sentences: |
| |
| 42 is a multiple of 6. |
| |
| Line l is parallel to line m. |
| |
| 10 is greater than 7. |
| |
| In each case the first element is related to the last element by the relation in italics. The two elements named are members of two separate sets, say set A and set B. |
| |
If  and  we obtain a set of ordered pairs (x, y). Thus a relation forms a set of ordered pairs. |
| |
|
| |
If A and B are two non-empty sets, then a relation R in A x B is a subset of A x B. If we use the letter R to denote a relation, then we can write the relation between a and b as aRb  a is related to b. |
| |
 |
| |
| Let R mean 'is greater than', then xRy means x > y. |
| |
 |
| |
| If A = {1, 2, 3} and B = {3, 5} list the ordered pairs for each of the following relations: |
| |
(i)  |
| |
(ii)  |
| |
(iii)  |
| |
 |
| |
| A x B = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 3), (3, 5)} |
| |
(i)  |
| |
| = {(3, 3)} is the only pair which satisfies the relation x = y. |
| |
 |
| |
| R 'is equal to' is a subset of A x B. |
| |
(ii) S = {(x, y) : x, y  A x B, y = x + 2} |
| |
| = {(1, 3), (3, 5)}. These two pairs satisfy the relation y = x + 2. |
| |
(iii)  |
| |
| = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5)} |
| |
 |
| |
 Five pairs satisfy the relation x < y |
| |
|
R, S and T are all subsets of A x B, hence they are all relations. |
| |
|
| |
| The set of first elements in a relation is called Domain. |
| |
| In example (6), Domain is set A = {1, 2, 3}. |
| |
|
| |
| The set of second elements in a relation is called Range. |
| |
| In example (6), Range is set B = {3, 5}. |
| |
|
|
| |
|
|
| |
|
|
|
|
|
Get FREE Live Tutoring
(No credit card required)
Customer Care
Click to get customer service, technical support and subscription help.
Refer-A-Friend
Get One Month Free!
When you refer a friend
Ordered Pairs and Cartesian Product
|
|
|
