Consider the relation R on the real numbers where xRy if and only if xy = 1.
(a) What is R^2 ? (b) What is R^3 ? (c) What is R^i for i ≥ 1? (d) What is R^∗ ?
I really don't understand the concept. can you explain it with details?
Consider the relation R on the real numbers where xRy if and only if xy =...
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if a) x + y = 0 b) x= ±y. c) x-y is a rational number. d) = 2y. e) xy ≥ 0. f) xy = 0. g) x=l. h) r=1 or y = 1
4. Consider the relation on the positive integers xRy if and only if x x+y (a) List three ordered pairs from this relationship (b) Is R reflexive? Prove your answer (c) Is R symmetric? Prove your answer (d) Is R anti-symmetric? Prove your answer (e) Is R transitive? Prove your answer.
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?
A is the binary relation defined on real numbers as follows. For all real numbers 1, 39 XAy if and only if xy >0. Determine if A is reflexive, symmetric, transitive, antia symmetric.
Consider the relation R(A, B, C, D, E), where it is known that the only keys are {A, C, D} and {D, E}: Give a set of functional dependencies that will make {A, C, D} and {D, E} be the only keys of R. This set should be such that if you delete any FD, then the keys of R will be something other than {A, C, D} and {D, E}.
10. [12 Points) Properties of relations Consider the relation R defined on R by «Ry x2 - y2 = x - y (a) Show that R is reflexive. (b) Show that R is symmetric. (c) Show that R is transitive. (d) You have thus verified that R is an equivalence relation. What is the equivalence class of 3? (e) More generally, what is the equivalence class of an element x? Use the listing method. (f) Instead of proving the three...
The domain of the relation L is the set of all real numbers. Forx, y E R, xLy if xy. L is O transitive not transitive D Question 5 1 pts Assume that (a, b), (b, c), (c, d), (d, e), and (e, a) are edges in a digraph. <a, b, c, d, e,a> is a? There may be multiple answers. O walk circuit path cycle
For each of the following relations on the set of all real numbers, decide whether or not the relation is reflexive, symmetric, antisymmetric, and/or transitive. Give a brief explanation of why the given relation either has or does not have each of the properties. (x, y) elementof R if and only if: a. x + y = 0 b. x - y is a rational number (a rational number is a number that can be expressed in the form a/b...
3. For the following question, we only consider subsets of the set R of real numbers. In particular, for any set of real numbers S, we have S-R- S For each of the following, write out the resulting set using set-builder notation in the style above i.e., by describing the range(s) of values) (b) GnH (d) GUH
Let X = R × R. We define the preference relation R on X, where (a, b)R(c, d) if a >c or b> d. a. Can you define a utility function so, find a utility function. If not, explain why not. on X which represents the preference relation R? If : {(1,5), (2, 5), (3, 5), (4, 5), . .}. Can you define a utility function u on X which represents the preference relation R? If so, find a utility...