Question

Let P = {(1, 4),(3, 5),(4, 1)}, Q = {(1, 5),(2, 2),(3, 4),(5, 2)} and R ={(4, 4),(2, 1),(5, 3),(3, 4)}.

Find P ◦ Q ◦ R

Answer 1

Given,

$P = \{(1, 4),(3, 5),(4, 1)\},~ Q = \{(1, 5),(2, 2),(3, 4),(5, 2)\} ~\text{and~} \\R =\{(4, 4),(2, 1),(5, 3),(3, 4)\}.$

$\text{Since~}(3,4)\in Q, (4,1) \in P,~ P \circ Q = \{(3,1)\}$

$P \circ Q \circ R = \{(5,1)\}$ since $(5,3)\in R, (3,1)\in P\circ Q$.