Question

Let A = {p. q, r, s} and B = {1, 2, 3}. Which of the following relations from A to B is not a function?
(i) $R_1=\left\{\right(p,1),(q,2),(r,1),(s,2\left)\right\}$
(ii) $R_2=\left\{\right(p,1),(q,1),(r,1),(s,1\left)\right\}$
(iii) $R_3=\left\{\right(p,1),(q,2),(r,1),(s,2\left)\right\}$
(iv) $R_4=\left\{\right(p,2),(q,3),(r,2),(s,2\left)\right\}$

Answer 1

We have,
A = {p, q, r, s} and B = {1, 2, 3}

(i) Now,
$R_1=\left\{\right(p,1),(q,2),(r,1),(s,2\left)\right\}$
$R_1$ is a function.

(ii) Now,
$R_2=\left\{\right(p,1),(q,1),(r,1),(s,1\left)\right\}$
$R_2$ is a function.

(iii) Now,
$R_3=\left\{\right(p,1),(q,2),(p,2),(s,3\left)\right\}$
$R_3$ is not a function because an element $pϵA$ is associated to two elements 1 and 2 in B.

(iv) Now,
$R_4=\left\{\right(p,2),(q,3),(r,2),(s,2\left)\right\}$
$R_4$ is a function.