Discrete math relation properties. For <= relation on the set of integers, specify if <= is Reflexive(R), Antireflexive(AR), Symmetric(S), Antisymmetric(AS), or Transitive(T). Show your analysis.

Quessyrutty6w 2022-07-15 Answered
Discrete math relation properties
I am working on a homework assignment and I am having trouble understanding the problem. I feel as if my professor forgot part of the problem, but I would just like to double check and make sure I am not reading the problem incorrectly. This is the problem:
For relation on the set of integers, specify if is Reflexive(R), Antireflexive(AR), Symmetric(S), Antisymmetric(AS), or Transitive(T). Show your analysis.
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Answers (2)

Quenchingof
Answered 2022-07-16 Author has 14 answers
Step 1
It is reflexive (and therefore not anti-reflexive) since it's true for all elements that x x (since x = x is true for all integers). It's not symmetric however, since if x y is true then y x if false (unless x = y).
Step 2
It is anti-symmetric since ( x y y x ) x = y (i.e. x and y are the same integer). Finally, it would be transitive because x y and y z implies that x z.

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Ibrahim Rosales
Answered 2022-07-17 Author has 7 answers
Step 1
- The relation is reflexive. To see this, consider some x Z . Then, x x, by definition of .
- By definition of anti-reflexive, is not antireflexive.
- The relation is not symmetric, as if x y, y x.
- The relation is antisymmetric, as if x y and y x, then y = x.
Step 2
- This is transitive, as if x y z, then x z.

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