Question

Let V={1,2,3,4} and let f={(1,3),(2,1),(3,4),(4,3)} and g={(1,2),(2,3),(3,1),(4,1)}. Find f o g.

Answer 1

Answer on Question#38064 – Math - Abstract Algebra:

Let $V = \{1,2,3,4\}$ and let $f = \{(1,3),(2,1),(3,4),(4,3)\}$ and $g = \{(1,2),(2,3),(3,1),(4,1)\}$. Find $f \circ g$.

Solution.

$$(f \circ g)(1) = f(g(1)) = f(2) = 1;$$ $$(f \circ g)(2) = f(g(2)) = f(3) = 4;$$ $$(f \circ g)(3) = f(g(3)) = f(1) = 3;$$ $$(f \circ g)(4) = f(g(4)) = f(1) = 3;$$

Hence:

$$f \circ g = \{(1,1),(2,4),(3,3),(4,3)\}.$$