Relations

Represent each of these relations on {1, 2, 3} with a matrix (with the elements of this set listed in increasing order)

Relations /

Recap: A relation R can be represented as a zero-one matrix. If (ai,bj)∈R, then we write a 1 in the matrix in the position (i,j). Otherwise, we write a 0. The size of the matrix will be determined by the size of the set. If you have a relation R on the set A={1,2,3}, the […]

Represent each of these relations on {1, 2, 3} with a matrix (with the elements of this set listed in increasing order) Read More »

Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a,b)∈R if and only if

Relations /

Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈ A.” Definition: “A relation R on a set A is called symmetric if (b,a) ∈ R whenever (a,b) ∈ R, for all a,b ∈ A. A relation R on a set A such that for

Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a,b)∈R if and only if Read More »

Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) ∈ R if and only if 

Relations /

As usual, let’s start with relevant definitions. Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈ A.” Definition: “A relation R on a set A is called symmetric if (b,a) ∈ R whenever (a,b) ∈ R, for all a,b ∈ A. A relation R

Determine whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) ∈ R if and only if  Read More »

For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.

Relations /

Let’s start by reviewing the relevant definitions needed to solve this type of exercise. Definition: “Let A and B be sets. A binary relation from A to B is a subset of A × B.” Definition: “A relation R on a set A is called reflexive if (a,a) ∈ R for every element a ∈

For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. Read More »

List the ordered pairs in the relation R from A = {0,1,2,3,4} to B = {0,1,2,3}, where (a,b) ∈ R if and only if

Relations /

Definition: “Let A and B be sets. A binary relation from A to B is a subset of A × B.” Discrete Mathematics and its Applications by Rosen. From the definition above, we can easily see that in a binary relation from A to B, the first element will belong to A and the second

List the ordered pairs in the relation R from A = {0,1,2,3,4} to B = {0,1,2,3}, where (a,b) ∈ R if and only if Read More »