Answer to Question #185893 in Discrete Mathematics for gamesexperience

Question

Let S={2, 4, 7}

and T={1, 3, 5}

. Find f(S×T)

if  

• f(x,y)=14x/3y
•  

Answer 1

Let $S=\{2, 4, 7\}$ and $T=\{1, 3, 5\}$, $f(x,y)=\frac{14x}{3y}.$

Let us find $S×T:$

$S×T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(7,1),(7,3),(7,5)\}$ .

Let us find $f(S×T):$

$f(2,1)=\frac{28}{3}, f(2,3)=\frac{28}{9}, f(2,5)=\frac{28}{15}, f(4,1)=\frac{56}{3}, f(4,3)=\frac{56}{9},$

$f(4,5)=\frac{56}{15}, f(7,1)=\frac{98}{3}, f(7,3)=\frac{98}{9}, f(7,5)=\frac{98}{15}.$

It follows that $f(S×T)=\{\frac{28}{3}, \frac{28}{9}, \frac{28}{15}, \frac{56}{3}, \frac{56}{9},\frac{56}{15}, \frac{98}{3}, \frac{98}{9}, \frac{98}{15}\}.$