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Relations

S = {0, 1, 2, 4, 6}

Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetric and transitive closure of each relations.

A)
P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) }

B)
P {(0,1), (1,0), (2,4), (4,2), (4,6), (6,4)}

C)
P ((0,0), (1,1), (2,2), 4,4), (6,6), (4,6), (6,4)}

D)
P = everything not equal to 0

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S = {0, 1, 2, 4, 6}

Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetric and transitive closure of each relation.

A)
P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) }
Solution: (1) Reflexivity
Yes. Since for ,
So, the reflexive closure of P is itself.
(2) Symmetry
No. Since , but
So, the symmetric closure of P is
P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1),(1,0), (1,2),(2,1), (2,4), (4,2),(4,6),(6,4) }

(3) Antisymmetry
Yes, since it is NOT symmetric
(4) ...

Solution Summary

This is a test with binary relations for reflexivity, symmetry ,antisymmetry, and transitivity; and the reflexive, symmetric and transitive closure of each relations.

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