Question

Let X = {1,2,3,4,5} and Y = {1,3,5,7,9}. Which of the following is/are relations from X to Y

• A. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
• B. $R_4=\left\{\right(1,3),(2,5),(2,4),(7,9\left)\right\}$
• C. $R_1=\left\{\right(x,y):y=2+x,x\in X,y\in Y\}$
• D. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$

Answer 1

Answer: (A), (C), (D)

$R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$

If 'R' is a relation from 'A' to 'B' , then 'R' is defined as {(x,y): x$\in$ A and y$\in$ B}

In all the ordered pairs in the relations of R${}_1$, R${}_2$, R${}_3$ first component $\in$ X and second component $\in$ Y. So, R${}_1$, R${}_2$, R${}_3$are relations from X to Y.

$R_4$ is not a relation from X to Y , because in the ordered pair (7,9), the first component 7 $\notin$ X.