Problem-43
a) List all the ordered pairs in the relation R={(a,b)|adividesb} on the set {1,2,3,4,5,6}.
Write the ordered pairs in increasing order of a and then b, separated by commas without any spaces. For example, (1,2),(1,4),(2,3),(3,4),(3,5).
b) If the relation was represented graphically, which values would be connected?
Select all the values that each number on the left would be connected to on the right.
c) Display this relation in tabular form.
Select x in the appropriate entries, and leave the other entries blank.
Solution
a) (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,2),(2,4),(2,6),(3,3),(3,6),(4,4),(5,5),(6,6) .
b)
| 1x | 1 | 1 | 1 | 1 | 1 |
| 2x | 2x | 2 | 2 | 2 | 2 |
| 3x | 3 | 3x | 3 | 3 | 3 |
| 4x | 4x | 4 | 4x | 4 | 4 |
| 5x | 5 | 5 | 5 | 5x | 5 |
| 6 | 6x | 6x | 6 | 6 | 6x |
c)
|
R |
1 |
2 |
3 |
4 |
5 |
6 |
|
1 |
x |
x |
x |
x |
x |
x |
|
2 |
x |
x |
x |
|||
|
3 |
x |
x |
||||
|
4 |
x |
|||||
|
5 |
x |
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|
6 |
x |