Question

1. an arrow - diagram is a visual representation of a relation on finite sets. do the points in an arrow - diagram represent the ordered pairs in the relation? yes no they represent the sets they represent the cartesian product 2. let a = {2, 3, 8}. define the relation r between a and a such that (a, a) ∈ r if x is an integer multiple of a. is (8, 3) ∈ r true or false? multiple choice 1 point true false 3. if a matrix representation for a relation r on a finite set has a 1 at position (i, j), it means that the element corresponding to row i is related to the element corresponding to column j. multiple choice 1 point true false

Explanation:

1. First Question

An arrow - diagram of a relation on finite sets represents the ordered pairs in the relation. The points in the arrow - diagram represent the elements of the sets involved in the relation, not the Cartesian product directly. The Cartesian product is the set of all possible ordered pairs from two sets, while the relation is a subset of the Cartesian product.

Step1: Check the multiple condition

We need to check if 8 is an integer multiple of 3. To do this, we divide 8 by 3. The result of $8\div3=\frac{8}{3}\approx2.67$, which is not an integer.

In a matrix representation of a relation $R$ on a set, if there is a '1' at position $(i, j)$, it means that the element corresponding to row $i$ is related to the element corresponding to column $j$ according to the relation $R$. This is the standard way of representing a relation using a matrix for a finite - set relation.

Answer:

No

2. Second Question