(a) Construct a phrase-structure grammar that generates allsigned decimal numbers, consisting of a sign (either + or -), a nonnegative integer; and a decimal fraction that is either the empty string or adecimal point followed by a positive integer,where the initial zeros in an integerare allowed.

(b) Give the Backus-Naur form for this grammar.

(c) Construct a derivation tree for-31.4 inthis grammar.