Write recursive Prolog predicates to determine if a list of letters satisfies the following regular expressions or grammar rules. Use pattern matching.

a⁺ listOfa(L) returns true only if L is a list of one or more as

b ⁺ listOfb(L) returns true only if L is a list of one or more bs

c⁺ listOfc(L) returns true only of L is a list of one or more cs

a⁺b⁺ listOfab(L) returns true only if L is a list of as followed by bs

a⁺b⁺c⁺listOfabc (L) returns true only if L matches the pattern a⁺b⁺c⁺

bba^*bbb regExpr1(L) returns true only if L matches the pattern bba^*bbb

(aa |cc)⁺regExpr2(L) returns true only if L matches the pattern (aa | cc)⁺

a^*b^*c^* regExpr3(L) return true only if L matches pattern a^*b^*c^*

aⁿbaⁿ gRule1(L) returns true only if L is of the form aⁿbaⁿ for n >=0