Question

If A={a,b,c,d}, B={1,2,3}, find whether or not the following sets of ordered pairs are
 relations from A to B or not
(a)${R_1}$={(a,1),(a,3)}
(b)${R_2}$={(b,1),(c,2),(d,1)}
(c)${R_3}$={(a,1),(b,2),(3,c)}

Answer 1

Hint-If a relation is from A to B it will have the first element in the ordered pair from set A and second element from set B
The set of ordered pairs which are relations from set A to B are
D={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3),(c,1),(c,2),(c,3),(d,1),(d,2),(d,3)}
Now, if we look at the relations, we have
${R_1}$={(a,1),(a,3)} , now these ordered pairs in ${R_1}$ are a part of set D which consists of ordered pairs of relations from set A to B. So, ${R_1}$ is a relation from set A to B.
${R_2}$={(b,1),(c,2),(d,1)} ,now these ordered pairs in ${R_2}$are a part of set D which consists of ordered pairs of relations from set A to B. So, ${R_2}$ is a relation from set A to B.
${R_3}$={(a,1),(b,2),(3,c)}, now these ordered pairs in ${R_3}$ are not a part of set D which consists of ordered pairs of relations from set A to B. So, ${R_3}$ is not a relation from set A to B.

Note: To solve these type of questions first write down the set of all ordered pairs which are
 relations from A to B and then compare them with the options given so that it will be easy to
 figure out the correct option of the ordered pairs.