Question

In Exercises 24-31, determine whether each relation defined on the set of positive integers is reflexive, symmetric, antisymmetric, transitive, and/or a partial order. 24. (x, y) ? R if x = y². 25. (x, y) ? R if x > y. 26. (x, y) ? R if x ? y. 27. (x, y) ? R if x = y. 28. (x, y) ? R if 3 divides x - y. 29. (x, y) ? R if 3 divides x + 2y. 30. (x, y) ? R if x - y = 2. 31. (x, y) ? R if |x - y| = 2.

          In Exercises 24-31, determine whether each relation defined on
the set of positive integers is reflexive, symmetric, antisymmetric,
transitive, and/or a partial order.
24. (x, y) ? R if x = y².
25. (x, y) ? R if x > y.
26. (x, y) ? R if x ? y.
27. (x, y) ? R if x = y.
28. (x, y) ? R if 3 divides x - y.
29. (x, y) ? R if 3 divides x + 2y.
30. (x, y) ? R if x - y = 2.
31. (x, y) ? R if |x - y| = 2.

In Exercises 24-31, determine whether each relation defined on
the set of positive integers is reflexive, symmetric, antisymmetric,
transitive, and/or a partial order.
24. (x, y) ? R if x = y².
25. (x, y) ? R if x > y.
26. (x, y) ? R if x ? y.
27. (x, y) ? R if x = y.
28. (x, y) ? R if 3 divides x - y.
29. (x, y) ? R if 3 divides x + 2y.
30. (x, y) ? R if x - y = 2.
31. (x, y) ? R if |x - y| = 2.

Added by Michael M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert George Prestidge

06/30/2024

Step 1

(x,y) ∈ R if x = y Reflexive: Yes, because x = x for all x. Symmetric: Yes, because if x = y, then y = x. Antisymmetric: Yes, because if x = y and y = x, then x = y. Transitive: Yes, because if x = y and y = z, then x = z. Partial Order: Yes, because it is Show more…

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In Exercises 24-31, determine whether each relation defined on the set of positive integers is reflexive, symmetric, antisymmetric, transitive, and/or a partial order: 24. (x,y) ∈ R if x = y² 25. (x,y) ∈ R if x > y 26. (x,y) ∈ R if x ≥ y 27. (x,y) ∈ R if x = y 28. (x,y) ∈ R if 3 divides x - y 29. (x,y) ∈ R if 3 divides x + 2y 30. (x,y) ∈ R if x - y = 2 31. (x,y) ∈ R if |x - y| = 2