Set A = {1, 2, 3, 4}, write a binary relation R on A that is...

Set A = {1, 2, 3, 4}, write a binary relation R on A that is reflexive, symmetric and transitive, with (1, 2),(3, 2) ∈ R.

Expert Solution

Here A = { 1,2,3,4 }.

Now we define a binary relation R on A , then R must a subset of A × A.

R = { (1 ,1 ), (2, 2), (3, 3) , (4, 4), (1, 2), (2, 1), (2, 3), (3,2) }.

As R is subset of A × A , therefore it is a binary relation on A with , (1, 2), (3, 2) R.

Clearly ,R is reflexive as for all x A, (x, x)R.

R is also symmetric relation as if (x, y) R (y, x) R for x ,y are member of A.

For any (x, y) R and (y, z) R (x, z) R , for x, y, z are member of A.

Another relation on A can be defined as -

R = { ( 1,1), (2, 2), (3, 3), (4, 4), ( 1, 2) , (2, 1), (2, 3), ( 3, 2), ( 2, 4), (4, 2)}.

This relation R is also reflexive, symmetric and transitive , with ( 1, 2), (3, 2) R.

Colby Messinger answered 7 months ago

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by...

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by R = {(1, 1),(1, 3),(2, 2),(2, 4),(2, 5),(3, 1),(3, 3),(4, 2),(4, 4),(4, 5),(5, 2),(5, 4),(5, 5)}. (a) Draw the digraph which represents R. (b) Give the 0 -1 matrix of R with respect to the natural ordering. (c) Which of the five properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does R have? Give a brief reason why or why not each property holds. 2. Let...

1. Write the set { x | x ∈ R, x2 = 4 or x 2...

1. Write the set { x | x ∈ R, x2 = 4 or x 2 = 9} in list form. 2. {x: x is a real number between 1 and 2} is an a) finite set b) empty set c) infinite set 3. Write set {1, 5, 15, 25,…} in set-builder form. 4. What is the cardinality of each of these sets? a) {{a}} b) {a, {a}} c) {a, {a}, {a, {a}}} d) {∅} e) {∅, {∅}, {∅, {∅}}}...

Let S = {-3, -2, -1, 0, 1, 2, 3}. Define a relation R on S...

Let S = {-3, -2, -1, 0, 1, 2, 3}. Define a relation R on S by: xRy if and only if x = y + 4n for some integer n. a) Prove that R is an equivalence relation. b) Find all the distinct equivalence classes of R.

(6) Define a binary operation ∗ on the set G = R^2 by (x, y) ∗...

(6) Define a binary operation ∗ on the set G = R^2 by (x, y) ∗ (x', y') = (x + x', y + y'e^x) (a) Show that (G, ∗) is a group. Specifically, prove that the associative law holds, find the identity e, and find the inverse of (x, y) ∈ G. (b) Show that the group G is not abelian. (c). Show that the set H= (x*x=e) is a subgroup of G.

Show that the given relation R is an equivalence relation on set S. Then describe the...

Show that the given relation R is an equivalence relation on set S. Then describe the equivalence class containing the given element z in S, and determine the number of distinct equivalence classes of R. Let S be the set of all possible strings of 3 or 4 letters, let z = ABCD and define x R y to mean that x has the same first letter as y and also the same third letter as y.

Let R be the relation on the set of people given by aRb if a and...

Let R be the relation on the set of people given by aRb if a and b have at least one parent in common. Is R an equivalence relation? (Equivalence Relations and Partitions)

Let R be a relation on a set that is reflexive and symmetric but not transitive?...

Let R be a relation on a set that is reflexive and symmetric but not transitive? Let R(x) = {y : x R y}. [Note that R(x) is the same as x / R except that R is not an equivalence relation in this case.] Does the set A = {R(x) : x ∈ A} always/sometimes/never form a partition of A? Prove that your answer is correct. Do not prove by examples.

Let R be a relation on the set of all integers such that aRb if and...

Let R be a relation on the set of all integers such that aRb if and only if 3a − 5b is even. Tell if R is an equivalence relation. Justify your answer. (Hint: 3b − 5a = 3a − 5b + 8b − 8a)

Determine if the following set W spans R^3 . W = {(1, 3, 1),(2, 1, 1),(−1,...

Determine if the following set W spans R^3 . W = {(1, 3, 1),(2, 1, 1),(−1, 0, 1)}

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and...

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and B at the point corresponding to ? = 1. (b) Find the equation of the osculating plane at the point corresponding to ? = 1. (c) Find the equation of the normal plane at the point corresponding to ? = 1

Question