$2\mathrm{.}1$ Recall the CFG G$4$ that we gave in Example $2\mathrm{.}4.$ For convenience, let$$s rename its

variables with single letters as follows.

E $->$E$+$T $|$T

T $->$T xF$|$F

F $->($E$)|$a

Give parse trees and derivations for each string.

a$.$ a

b$.$ a$+$a

$2\mathrm{.}2$

c$.$ a$+$a$+$a

d$.(($a$))$

a$.$ Use thelanguages A $=\{$ambncn$|$m$,$n $>=0\}$ and B $=\{$anbncm$|$m$,$n $>=0\}$

together with Example $2\mathrm{.}36$ to show that the class of context$-$free languages

is not closed under intersection.

b$.$ Use part $($a$)$ and DeMorgan$$s law $($Theorem $0\mathrm{.}20)$ to show that the class of

context$-$free languages is not closed under complementation.