5. Five marks exercise problems II

1. A relation \(\mathbb{R}\) is given by the set $\left\{(x,y)/y=x+3,x\in \{0,1,2,3,4,5\}\right\}$. Determine its domain and range.

 

 

2. Study the relations given below in set-builder form. Represent each of them by (a) an arrow diagram, (b) a graph, or (c) a set in roster form, wherever possible.

 

(i) \(\{(x,y)|x = 2y, x \ in \{2,3,4,5\}, y \in \{1,2,3,4\}\}\)

 

(ii) \(\{(x,y)|y = x + 3, x, y \ \text{are natural numbers} < 10\}\)

 

Answer:

 

(i) \(\{(x,y)|x = 2y, x \ in \{2,3,4,5\}, y \in \{1,2,3,4\}\}\)

 

(a) an arrow diagram:

 

 

(b) a graph:

 

 

(c) Roster form: $\left\{\left(i,i\right),\left(i,i\right)\right\}$