Question

Let $A=\{1,2,3,4\}$ and $B=\{x,y,z\}$. Consider the subset $R=\left\{\right(1,x),(1,y),(2,z),(3,x\left)\right\}$of $A\times B.$ Is R, a relation from A to B? If yes, find domain and range of R. Draw arrow diagram of R and represent R in a tabular form.

Answer 1

Since every subset of $A\times B$ is a relation from A to B, therefore, R is also a relation
from A to B.
Domain of $R=\{1,2,3\}$Range of R $=\{x,y,z\}$
Arrow diagram of R in the tabular form, we construct a box with the help of $\left\{n\right(A)+2\}$ horizontal lines and $\left\{n\right(B)+2\}$ vertical lines. In this case, we draw 6 horizontal lines and 5 vertical lines to get 20 boxes $\left\{n\right(A)+1\}\times \left\{n\right(B)+1\}$ in general). Place R in the extreme left top and elements of A below R in a vertical line. Write elements of B in the first horizontal line as shown.
As $(1,x)\in R,$ place 1 in the row containing x. As $(1,z)\notin R,$ place 0 on the row containing 1 and column containing z. Complete the table corresponding to other pairs also. Here, we use the convention that if $(a,b)\in R,$ we write '1' in the row containing a and column containing b and if $(a,b)\notin R,$ we write '0' in the corresponding box.