Question

1. We define a relation C on the set of humans as xRy ⇐⇒ x and...

1. We define a relation C on the set of humans as xRy ⇐⇒ x and y were born in the same country

Describe the equivalence class containing yourself as an element.

2. Let R be an equivalence relation with (x, y) ∈ R and (y, z) is not ∈ R (that is, y does not relate to z). Can you determine whether or not xRz? Why or why not?

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
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.
Consider the following relation on the set Z: xRy ? x2 + y is even. For...
Consider the following relation on the set Z: xRy ? x2 + y is even. For each question below, if your answer is "yes", then prove it, if your answer is "no", then show a counterexample. (i) Is R reflexive? (ii) Is R symmetric? (iii) Is R antisymmetric? (iv) Is R transitive? (v) Is R an equivalence relation? If it is, then describe the equivalence classes of R. How many equivalence classes are there?
For natural numbers x and y, define xRy if and only if x^2 + y is...
For natural numbers x and y, define xRy if and only if x^2 + y is even. Prove that R is an equivalence relation on the set of natural numbers and find the quotient set determined by R. What would the quotient set be? can this proof be explained in detail?
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 A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A as follows : For all...
Let A = {1,2,3,4,5,6,7,8,9,10} define the equivalence relation R on A as follows : For all x,y A, xRy <=> 3|(x-y) . Find the distinct equivalence classes of R(discrete math)
Let A={1,2,3,4,5,6} and let R be the relation on A defined by xRy iff x +...
Let A={1,2,3,4,5,6} and let R be the relation on A defined by xRy iff x + y is even and x is less than or equal to y. Determine if R is partial order.
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,...
Let R = {(x, y) | x − y is an integer} be a relation on...
Let R = {(x, y) | x − y is an integer} be a relation on the set Q of rational numbers. a) [6 marks] Prove that R is an equivalence relation on Q. b) [2 marks] What is the equivalence class of 0? c) [2 marks] What is the equivalence class of 1/2?
Suppose we define the relation R on the set of all people by the rule "a...
Suppose we define the relation R on the set of all people by the rule "a R b if and only if a is Facebook friends with b." Is this relation reflexive?  Is is symmetric?   Is it transitive?   Is it an equivalence relation? Briefly but clearly justify your answers.
Problem 3 For two relations R1 and R2 on a set A, we define the composition...
Problem 3 For two relations R1 and R2 on a set A, we define the composition of R2 after R1 as R2°R1 = { (x, z) ∈ A×A | (∃ y)( (x, y) ∈ R1 ∧ (y, z) ∈ R2 )} Recall that the inverse of a relation R, denoted R -1, on a set A is defined as: R -1 = { (x, y) ∈ A×A | (y, x) ∈ R)} Suppose R = { (1, 1), (1, 2),...