Prove that NPNP$\backslash$coNP $=$ NP$.$ Be sure you understand what this means. A language is in NPNP$\backslash$coNP if it can

be written in the form f$$ j $9$ : $=1$g$,$ where $$ is a poly$-$time oracle TM$,$ and $$ is a language

in NP $\backslash$ coNP. In other words, $$ has both an $$NP$-$style$$ algorithm and a $$coNP$-$style$$ one. More formally,

there are polytime TMs $1$ and $2$ such that $=$ f$$ j $91$ : $11=1$g $=$ f$$ j $82$ : $22=1$g$.$

Hint: compare the situation to NPNP or NPcoNP, both of which are equal to $\backslash$Sigma $2.$ Think about where the

additional quantier comes from in these cases, and why you might not need one in our problem