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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

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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

$2.19

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