Context free languages and Push-down automata

Consider the following languages. 

 Which one of the following statements is FALSE?

Which of the following pairs have DIFFERENT expressive power?

Let P be a regular language and Q be context-free language such that Q ⊆ P. (For example, let P be the language represented by the regular expression p*q* and Q be {pⁿ qⁿ  | n ∈ N}). Then which of the following is ALWAYS regular? 

(A) P ∩ Q 

(B) P - Q 

(C) ∑* - P 

(D) ∑* - Q

Consider the languages L1, L2 and L3 as given below.

LI= {0^P1^q |p, q∈N}

L2={0^p1^q |p, q∈ N and p=q} and

L3= {0^P1^q0^r |p, q, r∈ N and p =q = r}

Which of the following statements is NOT TRUE?

Consider the languages - 
L1 = {0ⁱ1^j | i != j}. 
L2 = {0ⁱ1^j | i = j}. 
L3 = {0ⁱ1^j | i = 2j+1}. 
L4 = {0ⁱ1^j | i != 2j}.

S -> aSa|bSb|a|b; The language generated by the above grammar over the alphabet {a,b} is the set of

Let L = L1∩L2, where L1 and L2 are languages as defined below:

L1 = {a^m b^m caⁿ bⁿ | m, n >= 0}

L2 = {aⁱ b^j c^k | i, j, k >= 0}

Then L is

Which of following statement(s) is/are not correct? (I) Languages generated by the grammar S→aSa ∣ aa is not regular. (II) Languages generated by the grammar S→aSb ∣ aa is not regular. (III) Languages generated by the grammar S→S1|S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n - m|, n≥0, m≥0, k≥0}. (IV) Languages generated by the grammar S→S1S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n - m|, n≥0, m≥0, k≥0}.

Consider the following languages.



L₁ = {aⁱ b^j c^k | i = j, k ≥ 1}

L₁ = {aⁱ b^j | j = 2i, i ≥ 0}

Which of the following is true?

Match the following: