Think about the not equal 6= relationship on the integers.

(a) Prove 6= is not transitive

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(b) Prove 1 6 = 2.

Based on your experience in problem 1, you might suspect that R2 is reflexive if a relation R to S is symmetric.

You can prove or disprove it.

Question 1

If we have a set of integers, it is possible to express non-equality among the integers.

The order of the integers is increasing, so… clearly proves that it is not transitive since

So,

Question 2

If the set has symmetry, the relation on to R will be.

R is symmetrical but is not part the relation so it is not reflexive

References

(2012, may 7).

(2017, July 19).

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