## Problem-43

**Problem-43**

**a)** List all the ordered pairs in the relation *R*={(*a*,*b*)|*a*divides*b*} 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 |
|||||

6 |
x |