Consider the language K = {aⁱ bⁱ : i N₀}.

Using the fact that K is not regular show that each of the following languages is not regular.

1. W = { aⁱ bⁱ: i N₀} {a⁵b⁵}

2. X = { aⁱ bⁱ: i N₀, i = 5} {ba}

3. Y = { aⁱ bⁱ: i N₀} (ab)

4. Z = { aⁱ bⁱ aj : i, j N₀, i 2}