3. Five marks example problems

1. Let \(A = \{1,2,3,7\}\) and \(B = \{3,0,-1,7\}\), which of the following are relation from \(A\) to \(B\)?

 

(i) \(R_1 = \{(2,1), (7,1)\}\) not a relation from A to Brelation from A to B

 

(ii) \(R_2 = \{(-1,1)\}\) not a relation from A to Brelation from A to B

 

(iii) \(R_3 = \{(2,-1), (7,7), (1,3)\}\) relation from A to Bnot a relation from A to B

 

(iv) \(R_4 = \{(7,-1), (0,3), (3,3), (0,7)\}\) not a relation from A to Brelation from A to B

 

2. Let \(A = \{1,2,3,4,...,45\}\) and \(R\) be the relation defined as "is square of" on \(A\). Write \(R\) as a subset of \(A \times A\). Also, find the domain and range of \(R\).

 

Answer:

 

\(\mathbb{R} =\) $\left\{\left(i,i\right),\left(i,i\right),\left(i,i\right),\left(i,i\right),\left(i,i\right),\left(i,i\right)\right\}$

 

Domain of \(\mathbb{R}\) \(=\) $\left\{i,i,i,i,i,i\right\}$

 

Range of \(\mathbb{R}\) \(=\) $\left\{i,i,i,i,i,i\right\}$