4. Consider the language F={aibjcki,j,k0 and if i=1 then j=k}. (a) Define F as a union of three languages, F0,F1,F2, respectively corresponding to the value/range of i, i.e., i=0,i=1, and i2. (b) For F0,F1,F2, answer the simple question whether they are regular or non-regular but contextfree. No proof necessary. (c) Prove that F is not regular by contradiction and the closure property under difference for regular languages. (d) Construct a context-free grammar for F, based on your answer to (a). Start the grammar with SS0S1S2 4. Consider the language F={aibjcki,j,k0 and if i=1 then j=k}. (a) Define F as a union of three languages, F0,F1,F2, respectively corresponding to the value/range of i, i.e., i=0,i=1, and i2. (b) For F0,F1,F2, answer the simple question whether they are regular or non-regular but contextfree. No proof necessary. (c) Prove that F is not regular by contradiction and the closure property under difference for regular languages. (d) Construct a context-free grammar for F, based on your answer to (a). Start the grammar with SS0S1S2