a$)$ Define the formal language $L_{\text{d}\text{i}\text{a}\text{g}}.$ b$)$ Is it true, that $L_{\text{d}\text{i}\text{a}\text{g}}$inRE $?$ c$)$ Is it true,

that $L_{\text{d}\text{i}\text{a}\text{g}}$inR $?$ d$)$ Is it true, that the complementary language of $L_{\text{d}\text{i}\text{a}\text{g}}$ is in R$?$

Why?

a$)$ Define NP$-$completeness. b$)$ State the theorem we have used several times for

proving NP$-$completeness of a language based on the already proven NP$-$completeness

of another language.