Question

5. Prove or disprove the following statements: (a) Let R be a relation on the set...

5. Prove or disprove the following statements:

(a) Let R be a relation on the set Z of integers such that xRy if and only if xy ≥ 1. Then, R is irreflexive.

(b) Let R be a relation on the set Z of integers such that xRy if and only if x = y + 1 or x = y − 1. Then, R is irreflexive.

(c) Let R and S be reflexive relations on a set A. Then, R − S is irreflexive.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Disprove: The following relation R on set Q is either reflexive, symmetric, or transitive. Let t...
Disprove: The following relation R on set Q is either reflexive, symmetric, or transitive. Let t and z be elements of Q. then t R z if and only if t = (z+1) * n for some integer n.
Let F = {A ⊆ Z : |A| < ∞} be the set of all finite...
Let F = {A ⊆ Z : |A| < ∞} be the set of all finite sets of integers. Let R be the relation on F defined by A R B if and only if |A| = |B|. (a) Prove or disprove: R is reflexive. (b) Prove or disprove: R is irreflexive. (c) Prove or disprove: R is symmetric. (d) Prove or disprove: R is antisymmetric. (e) Prove or disprove: R is transitive. (f) Is R an equivalence relation? Is...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y. For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3. (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
For Problems #5 – #9, you willl either be asked to prove a statement or disprove...
For Problems #5 – #9, you willl either be asked to prove a statement or disprove a statement, or decide if a statement is true or false, then prove or disprove the statement. Prove statements using only the definitions. DO NOT use any set identities or any prior results whatsoever. Disprove false statements by giving counterexample and explaining precisely why your counterexample disproves the claim. ********************************************************************************************************* (5) (12pts) Consider the < relation defined on R as usual, where x <...
Let R be the relation on the set of real numbers such that xRy if and...
Let R be the relation on the set of real numbers such that xRy if and only if x and y are real numbers that differ by less than 1, that is, |x − y| < 1. Which of the following pair or pairs can be used as a counterexample to show this relation is not an equivalence relation? A) (1, 1) B) (1, 1.8), (1.8, 3) C) (1, 1), (3, 3) D) (1, 1), (1, 1.5)
Let Z be the set of integers. Define ~ to be a relation on Z by...
Let Z be the set of integers. Define ~ to be a relation on Z by x~y if and only if |xy|=1. Show that ~ is symmetric and transitive, but is neither reflexvie nor antisymmetric.
Prove that the relation R on the set of all people, defined by xRy if x...
Prove that the relation R on the set of all people, defined by xRy if x and y have the same first name is an equivalence relation.
a) Let R be an equivalence relation defined on some set A. Prove using induction that...
a) Let R be an equivalence relation defined on some set A. Prove using induction that R^n is also an equivalence relation. Note: In order to prove transitivity, you may use the fact that R is transitive if and only if R^n⊆R for ever positive integer ​n b) Prove or disprove that a partial order cannot have a cycle.
Let A be the set of all integers, and let R be the relation "m divides...
Let A be the set of all integers, and let R be the relation "m divides n." Determine whether or not the given relation R, on the set A, is reflexive, symmetric, antisymmetric, or transitive.
Let us say that two integers are near to one another provided their difference is 2...
Let us say that two integers are near to one another provided their difference is 2 or smaller (i.e., the numbers are at most 2 apart). For example, 3 is near to 5, 10 is near to 9, but 4 is not near to 8. Let R stand for this is-near-to relation. (a) Write down R as a set of ordered pairs. Your answer should look like this: R = {(x, y) : . . .}. (b) Prove or disprove:...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT