We are given three subsets of numbers $,,\{0,...,\}$

$.$ Design an algorithm that runs in worst case time $\backslash$Theta $($log$())$

that checks if there exists numbers $1,2$

in $,$

$,$ respectively and number $3$

in $$

such that $1+2=3$

$.$

Hint: Convert the set $=\{0,1,...,\}$

into the polynomial $()$: $0+1++$

$.$ Suppose $(),()$

are polynomials obtained from the sets $,$

respectively, interpret what the product $()\backslash$times $()$

signifies. Use this to complete an algorithm for the problem at hand that runs in $$log$()$

time.