Consider the following languages.

L₁ = {wxyx | w, x, y ∈ (0 + 1)⁺}

L₂ = {xy | x, y ∈ (a + b)*, |x| = |y|, x ≠ y}

Which one of the following is TRUE?

Which of the following languages are undecidable? Note that $$\langle M\rangle $$ indicates encoding of the Turing machine M.

L₁ = $$\left\{ {\langle M\rangle |L\left( M \right) = \phi } \right\}$$
L₂ = $$\{ \langle M,w,q\rangle |$$ M on input w reaches state q in exactly 100 steps }
L₃ = { $$\langle M\rangle |$$ L(M) is not recursive }
L₄ = { $$\langle M\rangle |$$ L(M) contains at least 21 members }

Consider the following language.

L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}

The minimum number of states in a DFA that accepts L is ______.

Which one of the following regular expressions represents the set of all binary strings with an odd number of 1’s?