# Relations

Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity

A)

S = Q

X p Y <-> ABS(X) <= ABS(Y)

B)

S = Z

X p Y <-> x -y is an integral multiple of 3

C)

S = N

X P Y <-> X is odd

D)

S = Set of all squares in the place

S1 p S2 <-> length of side of S1 = length of side S2

E)

S = set of finite-length strings of characters

X p Y <-> number of characters in x = number of characters in y

https://brainmass.com/math/finite-element-method/test-binary-relations-22607

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Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity

A)

S = Q

X p Y <-> ABS(X) <= ABS(Y)

Solution. (1) Reflexivity

Yes, since

(2) Symmetry

Yes, since

(3) Antisymmetry

No, since , but if

(4) Transitivity

Yes, since , we have

B)

S = Z

X p Y <-> x -y is an integral multiple of 3

Solution. (1) Reflexivity

Yes, ...

#### Solution Summary

This shows how to test binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity