Question

Given two sets $A=\{1,2,3,4\}$ and $B=\{p,q,r,s\}.$ Which of the following relations is/are function(s).

Answer 1

Given two sets $A=\{1,2,3,4\}$ and $B=\{p,q,r,s\}.$
Now, for any relation to be a function, two conditions must be met:
a. Each and every element of $A$ should be matched with an element of $B$
b. Each element of $A$ should be matched with only one element of $B$
$R_1=\left\{\right(a,b):a\in A\&b\in B\}{R}_1=\left\{\right(1,p),(1,q),(1,r),\cdots ,(4,r\left)\right\}$
This is not a function as one element of $A$ is getting mapped with multiple elements of $B$
$R_2=\left\{\right(1,p),(3,p),(4,r\left)\right\}$
This is also not a function since $2\in A$ is not getting mapped with any elements of $B.$
$R_3=\left\{\right(1,q),(2,p),(3,s),(4,r\left)\right\}$
This is a function as both conditions are getting satsified.
$R_4=\left\{\right(1,p),(2,p),(3,s),(4,r\left)\right\}$
This is also a function as both conditions are getting satsified.