Provide non-deterministic finite automata accepting the following languages over the alphabet Σ = {a,b}. Note: For w ∈ Σ∗,σ ∈ Σ, we use nσ(w) to mean the number of letters σ in w. 1. L1 = {w ∈ Σ∗ : w contains the substring ababa} 2. L2 = {w ∈ Σ∗ : na(w) mod 2 = 1 or nb(w) mod 3 = 2} 3. L3 = {w ∈ Σ∗ : w starts and ends with the same letter} A proof of correctness is not required, but you must use non-determinism.

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Provide non-deterministic finite automata accepting the following languages over the alphabet Σ = {a,b}. Note: For w ∈ Σ,σ ∈ Σ, we use nσ(w) to mean the number of letters σ in w.

1. L1 = {w ∈ Σ : w contains the substring ababa}

2. L2 = {w ∈ Σ : na(w) mod 2 = 1 or nb(w) mod 3 = 2}

3. L3 = {w ∈ Σ : w starts and ends with the same letter}

A proof of correctness is not required, but you must use non-determinism.

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