$1.$ Use the techniques discussed in class $($back$-$substitution, inductive reasoning $$ either $$strong$$ induction using n or $$weak$$ induction using n $=2$k$)$

to give asymptotic upper and lower bounds for T$($n$),$ assuming T$($n$)$ is constant for n $2.$ Note: don$$t just use Master Theorem!

a$)$ T$($n$)=3$ T$($n$/2)+$ n lg n

b$)$ T$($n$)=2$ T$(+1$