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
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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.
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.
Last updated date: 19th Sep 2023
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