Answer questions $($a$)$ through $($c$)$ for the following grammar:

val ::$=$ number $|$ val pair

number ::$=$ digit$+$

pair ::$=$ number op $|$ number pair op

op ::$="+"|"-"|"*"|"/"$

digit ::$="0"|"1"|"2"|"3"|"4"|"5"|"6"|"7"|"8"|"9"$

Also consider the following mutation, which adds an additional rule to the grammar:

pair ::$=$ number op $|$ number pair op $|$ op number

$1.$ Which of the following strings can be generated by the $($unmutated$)$ grammar?

a$)42$

b$)42$

c$)4+2$

d$)42+$

e$)427-*$

f$)42-7*$

g$)42-7*+$

$2.$ Find a string that is generated by the mutated grammar, but not by the original grammar.