Question

Let A = {1,2,3,7} and B = {3,0,–1,7}, which of the following are relation from A to B ?

• A. R${}_1=\text{{(2,1), (7,1)}}$
• B. R${}_3=\text{{(2, –1), (7, 7), (1, 3)}}$
• C. R${}_2=\text{{(–1,1)}}$
• D. R${}_4=\text{{(7,–1), (0,3), (3,3), (0,7)}}$

Answer 1

The correct option is B R${}_3=\text{{(2, –1), (7, 7), (1, 3)}}$

$\therefore$ Cartesian Product of A and B is
A $\times$ B = {(1,3),(1,0),(1,-1),(1,7),(2,3),(2,0),(2,-1),(2,7),(3,3) (3,0),(3,-1),(3,7),(7,3),(7,0),(7,-1),(7,7)}

Relation is defined as the subset of A$\times$ B.

(i) (2,1) $\in$ R${}_1$, but (2,1) $\notin$ A$\times$B. Hence R${}_1$ is not a relation from A to B.

(ii) R${}_2$ = {(–1,1)}, but (–1,1) $\notin$ A$\times$B . So, R${}_2$ is not a relation from A to B.

(iii) R${}_3$ = {(2, –1), (7, 7), (1, 3)}, R₃ is a subset of A $\times$ B, Hence R${}_3$ is a relation from A to B.

(iv) R${}_4$= {(7,–1), (0,3), (3,3), (0,7)} but (0,3), (3,3), (0,7) $\notin$ A x B. Hence R${}_4$ is not a relation from A to B.