1) For the relation on the set {1, 2, 3, 4}, decide whether it is reflexive, whe

Question

1) For the relation on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. In order to get full credits. For example, if it’s not reflexive, you must state why it is not.

{(1, 1), (1, 2), (2, 3), (2, 4), (3, 2), (3, 3)}

Reflexive:

Symmetric:

Antisymmetric:

Transitive:

2) For the relation on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. In order to get full credits. For example, if it’s not reflexive, you must state why it is not. (10 points)

{(1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4), (4,4)}

Reflexive:

Symmetric:

Antisymmetric:

Transitive:

Explanation / Answer

1)

For relation to be reflexive ,(a,a) must be in the relation for all a in the set.

But we see: (2,2) is not there so it is not reflexive

(2,4) is there but not (4,2) hence not symmetric

(2,3) and (3,2) are there but 2 is not equal to 3 so it is not anti symmetric

(1,2) ,(2,3) are there but (1,3) is not hence not transitive.

2)

(a,a) is there for all a in the set hence it is reflexive

(1,2) is there but (2,1) is not there hence it is not symmetrc

(2,3) ,(3,2) are both there but 2 is not equal to 3 hence not antisymmetric

(1,2),(2,3) are there but not (1,3) hence not transitive.

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