Answer to Question #185757 in Discrete Mathematics for zain ul abdeen

Question

i) Let S={2,4,7} and T={1,3,5}. Find f(S×T) if

f(x,y)=⌊14x/3y⌋

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f(x,y)=x^2+y^3

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Note: No partial credit would be admissible in this question

Answer 1

S={2,4,7}, T={1,3,5}

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

(i) $f(x,y)=\dfrac{14x}{3y}$

So,

$f(S\times T)=$

$\dfrac{14(2)}{3(1)}+\dfrac{14(2)}{3(3)}+\dfrac{14(2)}{3(5)}+\dfrac{14(4)}{3(1)}+\dfrac{14(4)}{3(3)}+\dfrac{14(4)}{3(5)}+\dfrac{14(7)}{3(1)}+\dfrac{14(7)}{3(3)}+\dfrac{14(7)}{3(5)}$

Hence $f(S\times T)$ ={$\dfrac{28}{3},\dfrac{28}{9},\dfrac{28}{15},\dfrac{56}{3},\dfrac{56}{9},\dfrac{56}{15},\dfrac{98}{3},\dfrac{98}{9},\dfrac{98}{15}$ }

(ii) $f(x,y)=x^2+y^2$

$f(S\times T)$ ={

$(2^2+1^2),(2^2+3^2),(2^2+5^2),(4^2+1^2),(4^2+3^2),(4^2+5^2),\\(7^2+1^2),(7^2+3^2),(7^2+5^2)$ }

$F(S\times T)=$ {${5,13,29,17,25,41,50,58,74}$ }