Question

If A = {3,4,7,8} and B = {1,7,10} then, which of the following sets are relations from A to B?

• A. $R_1=\text{{(3,7), (4,7), (7,10), (8,1)}}$
• B. $R_2=\text{{(3,1), (4,12)}}$
• C. $R_3=\text{{(3,7), (4,10), (7,7), (7,8), (8,11)}}$
• D. $R_4=\text{{(8,10)}}$

Answer 1

Answer: (A), (D)

The correct options are
A $R_1=\text{{(3,7), (4,7), (7,10), (8,1)}}$
D $R_4=\text{{(8,10)}}$

Given, A = {3,4,7,8} and B = {1,7,10}
$\therefore$ Cartesian Product of A and B is
A $\times$ B = {(3,1), (3,7), (3,10), (4,1), (4,7), (4,10), (7,1), (7,7), (7,10), (8,1), (8,7), (8,10)}
(i)We note that, R${}_1\subseteq$ A$\times$B . Thus,
R${}_1$is a relation from A to B.
(ii) (4,12) $\in$ R${}_2$ , but (4,12) $\notin$ A$\times$B . So, R${}_2$ is not a relation from A to B.
(iii) (7, 8) $\in$ R${}_3$ , but (7, 8) $\notin$ A$\times$B . So, R${}_3$ is not a relation from A to B.
(iv) R${}_4\subseteq$ A $\times$ B. Thus, R${}_4$ is a relation from A to B.