Choose the best answer: ANTI SYMMETRIC, TRANSITIVE RELATION, SYMMETRIC RELATION, REFLEXIVE RELATION
1. {(3,5)(5,3) (2,4)(4,5)}
2. {(3,1)(1,3)}
3. {(3,1)(2,3)(5,6)(6,5)}
4. {(1,3)(5,3)(7,5)}
5. {(8,9)(9,7)(8,7)}
6. {(4,2)(2,4)}
7. {(1,5)(2,5)(3,5)}
8. {(5,5)(5,6)(6,5)(6,6)(6,7)(7,6) (7,7)}
9. {(6,5)(5,4)(6,4)}
10. {(7,6)(6,5)(7,5)}
11. {(3,1)(1,3)}
12. {(4,3)(3,5)(4,5)}
13. {(6,6)(6,5)(5,5)(5,4)(4,4)}
14. {(6,5)(7,6)(4,5)(5,4)}
15. {(3,3)(4,4)(4,5)(5,4)(5,5)}
1. {(3,5)(5,3) (2,4)(4,5)}
We have but thus is not symmetric.
We have but thus is not antisymmetric.
Since and but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
2. {(3,1)(1,3)}
We have thus is symmetric.
We have but thus is not antisymmetric.
Since and but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
3. {(3,1)(2,3)(5,6)(6,5)}
We have but thus is not symmetric.
We have but thus is not antisymmetric.
Since and but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
4. {(1,3)(5,3)(7,5)}
We have but thus is not symmetric.
There is no pair of elements and with such that both and belong to the relation. Thus is antisymmetric.
Since and but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
5. {(8,9)(9,7)(8,7)}
We have but thus is not symmetric.
There is no pair of elements and with such that both and belong to the relation. Thus is antisymmetric.
Since and and the relation is transitive.
Since the relation is irreflexive, hence, it is not reflexive.
6. {(4,2)(2,4)}
We have thus is symmetric.
We have but thus is not antisymmetric.
Since and but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
7. {(1,5)(2,5)(3,5)}
We have but thus is not symmetric.
There is no pair of elements and with such that both and belong to the relation. Thus is antisymmetric.
The relation is transitive.
Since the relation is irreflexive, hence, it is not reflexive.
8. {(5,5)(5,6)(6,5)(6,6)(6,7)(7,6) (7,7)}
The relation is symmetric.
We have but thus is not antisymmetric.
The relation is transitive.
The relation is reflexive.
9. {(6,5)(5,4)(6,4)}
We have but thus is not symmetric.
There is no pair of elements and with such that both and belong to the relation. Thus is antisymmetric.
The relation is transitive.
Since the relation is irreflexive, hence, it is not reflexive.
10. {(7,6)(6,5)(7,5)}
We have but thus is not symmetric.
There is no pair of elements and with such that both and belong to the relation. Thus is antisymmetric.
The relation is transitive.
Since the relation is irreflexive, hence, it is not reflexive.
11. {(3,1)(1,3)}
We have thus is symmetric.
We have but thus is not antisymmetric.
Since and but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
12. {(4,3)(3,5)(4,5)}
We have but thus is not symmetric.
There is no pair of elements and with such that both and belong to the relation. Thus is antisymmetric.
The relation is transitive.
Since the relation is irreflexive, hence, it is not reflexive.
13. {(6,6)(6,5)(5,5)(5,4)(4,4)}
We have but thus is not symmetric.
The relation is antisymmetric.
Since but the relation is not transitive.
Since the relation is reflexive.
14. {(6,5)(7,6)(4,5)(5,4)}
We have but thus is not symmetric.
We have but thus is not antisymmetric.
Since but the relation is not transitive.
Since the relation is irreflexive, hence, it is not reflexive.
15. {(3,3)(4,4)(4,5)(5,4)(5,5)}
The relation is symmetric.
We have but thus is not antisymmetric.
The relation is transitive.
Since the relation is reflexive.
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