S1:Any language L over an alphabet Σ,L^+=L-{ϵ} is always TRUE.<- This statement is false as we are are taken L^+ on one side which means that the language L can be concatenated one or more time but not zero times. but on the Leeft hand side we are just taking the language once and removing epsilon from it .So this is false.
S2: Any language L over an alphabet Σ,L+=L^*-{ϵ} is always TRUE.<- This statement is true.
L^* means the kleene closure of a language i.e the language 0 or more times . In simpler words:
L^*={ϵ,L^1,L^2,L^3,L^4........}
L^+={L^1,L^2,L^3,L^4........}
So lhs=rhs i.e:Σ,L+=L^*-{ϵ}
Note: In statement 1 on the rhs we have just taken the language and in statement 2 on the rhs we have taken the kleene closure of the language . This is the difference between the two.
