$\backslash$table$[[$Entered$,$Answer Preview,Result$],[$xxcorrect$],[$yycorrect$],[$xxincorrect$],[$xxcorrect$],[20*$y$,20$y$,$correct$],[$yycorrect$],[20$yycorrect$],[20*$y$,20$y$,$correct$]]$Prove the following theorem by contrapositive: For any positive real numbers $x$ and $y,$ if $xy>400,$

then $x>20$ or $y>20.$

Hint: answer each blank with an expression. Type $"x^2{?}^{\text{'}\text{'}}$ for $"x".$

proof.

Let $x$ and $y$ be positive real numbers such that

and

Since

multiply both sides of

by $y$ yields $xy$

Mutiply both sides of

by $20$ yields

Since $xy$

$400,xy400.$