Please expand the grammar G1[E] as indicated below for all parts (A, B, and C):

A) Add the operator & to the following grammar. It should have higher precedence than *, lower precedence than + and be evaluated left to right.

B) Modify the grammar such that operator := has the lowest precedence and is evaluated right to left. Statements such as x := y := z should be legal. This operation is referred to as multiple assignment in languages such as C and Algol. While powerful, it is particularly dangerous if the variables are not of the same type.

C) Add parenthesis to the grammar such that they have the highest precedence with inner most parenthesis evaluated first.

G1[E]:

E ::= A := E1

E1 ::= F | E1 * F

F ::= A | F - A | F + A

A ::= x | y | z