Question

C. RELATION. Consider X = {-3, -2, -1, 0, 1} defined by (x,y) ∈ R if x≥ y.

Find for:

1. Elements of R (3 pts)

2. Domain and Range of R (2 pts)

3. Draw the digraph (3 pts)

4. Identify the properties of R (2pts)

Answer 1

Solution.

1.

$R=\{(x,y)|x\geq y\}=\{(1,1),(1,0),(1,-1),(1,-2),(1,-3),\newline(0,0),(0,-1),(0,-2),(0,-3),(-1,-1),(-1,-2),\newline(-1,-3),(-2,-2),(-2,-3),(-3,-3)\}.\newline 2.$

Domain(R)=$\{-3,-2,-1,0,1\}.$

Range(R)=$\{-3,-2,-1,0,1\}.$

3.

4.

Relation R is reflexive,
antusymmetric,
non-transitive.