3 For the equivalence relation on {0, 1,2,3,4} defined as {(x, y): z+y is even} (a) Write it out as a list of ordered pairs (b) List the cells in the associated partition.

Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.

23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.

13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.

2 Explain why the relation on N defined as is not an equivalence relation. {(x, y): x+y is a multiple of 3}

The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1, 00). Can X1, X2, X3 be equivalence classes with respect to some equivalence relation on R? O No, they can't be equivalence classes for some equivalence relation since X1n X2 + 0. O No, they can't be equivalence classes for some equivalence relation since any equivalence relation on infinite set has infinitely many different equivalence classes. O Yes, these sets can be equivalence classes for some equivalence relation since X1 U X2 U X3 = R. O Yes, these sets can be equivalence classes for some equivalence relation since X2n X3 = 0.

Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes but have no clue how and why, so please really explain step by step how they get there in detail,

Let A={5,10,15,20, 25} and a partition of A be: {5,25},{10, 20} , {15} (a) Write all pairs of the relation associated with the partition.

Please solve the screenshot, thank you!

Let R be the relation, {(a, b) € NxN: a + b² is divisible by 3} Give an example that shows that R is not symmetric. ER and R In each box enter an ordered pair of natural numbers less than 100. Include the parentheses and comma, as you do if you write an ordered pair on paper.