Let $f: \{1,3,4\} \rightarrow \{1,2,5\}$ and $g: \{1,2,5\} \rightarrow \{1,3\}$ be given by $f = \{(1,2), (3,5), (4,1)\}$ and $g = \{(1,3), (2,3), (5,1)\}$. Write down $g \circ f$.

(A) The functions $f: \{1,3,4\} \rightarrow \{1,2,5\}$ and $g: \{1,2,5\} \rightarrow \{1,3\}$ are defined as $f = \{(1,2), (3,5), (4,1)\}$ and $g = \{(1,3), (2,3), (5,1)\}$.
$(g \circ f)(1) = g(f(1)) = g(2) = 3$ [since $f(1) = 2$ and $g(2) = 3$]
$(g \circ f)(3) = g(f(3)) = g(5) = 1$ [since $f(3) = 5$ and $g(5) = 1$]
$(g \circ f)(4) = g(f(4)) = g(1) = 3$ [since $f(4) = 1$ and $g(1) = 3$]
Therefore,$g \circ f = \{(1,3), (3,1), (4,3)\}$.