Fsc Part 1 Mathematics (Complete Solution)

#
Q7

What operation is represented by the adjoining table? name the identy element of the relevant set, if it exists. Is the operation associative? Find the inverse of 0,1,2,3, if they exist.

* |
0 |
1 |
2 |
3 |

0 |
0 |
1 |
2 |
3 |

1 |
1 |
2 |
3 |
0 |

2 |
2 |
3 |
0 |
1 |

3 |
3 |
0 |
1 |
2 |

Solution:

1. The operation is addition mod 4.

2. ) is the identity element

3. The operation is a associative.

4. The inverse of 0 is 0,1 and 3 are inverses of each other. The inverse of 2 is 2.