Are the following languages contextfree or not If yes specif

Are the following languages context-free or not? If yes, specify a context-free grammar in BNF notation that generates the language. If not, give an informal argument. {a^nb^mc^0| m > 0, n greaterthanorequalto 0, o > 0} with alphabet sigma = {a, b, c} {a^nb^mc^0| m > n greaterthanorequalto 0, o > 0} with alphabet sigma = {a, b, c} {a^nb^mc^n| n > 0}, with alphabet sigma = {a, b, c} {a^2nb^3n | n greaterthanorequalto 0}, with alphabet sigma = {a, b, } {ww^R|w element sigma* and w^R is w in reverse}, with alphabet sigma = {a, b, } {a^nb^mc^md^n | n greaterthanorequalto 0, m greaterthanorequalto 0}, with alphabet sigma = {a, b, c} {a^nb^mc^nd^m | n greaterthanorequalto 0, m greaterthanorequalto 0}, with alphabet sigma = {a, b, c} {a^nb^mc^md^m | n greaterthanorequalto 0, m greaterthanorequalto 0}, with alphabet sigma = {a, b, c} {a^na^nb^nb^n | n greaterthanorequalto 0}, with alphabet sigma = {a, b, } {w|w has more than 5 symbols}, with alphabet sigma = {a, b, } Which of the languages are also regular languages, i.e., can be expressed by a regular expression? Prove it by giving the regular expression that specifies the language.

Solution

As per chegg olicy I will answer only top 3 questions:

In a context-free grammar, we can pair up the characters the way we do with brackets. example:

S --> aSb

S --> ab

1) Yes,

S--> aSb

S -->ab

S--> aSc

S-->ac

S-->bSc

S-->bc

2) Yes..

S--> aSb

S -->ab

S--> aSc

S-->ac

S-->bSc

S-->bc

3)

yes,

S--> aSb

S -->ab

S--> aSc

S-->ac

S-->bSc

S-->bc