Let = {0,1}. Let C 1 be the language of all strings that contain a 1

Let Σ = {0,1}. Let C₁ be the language of all strings that contain a 1 in their middle third. Let C₂ be the language of all strings that contain two 1s in their middle third. So C₁ = {xyz| x, z ∈ Σ^* and y ∈ Σ^*1Σ^*, where |x| = |z| ≥ |y|} and C₂ = {xyz| x, z ∈ Σ^* and y ∈ Σ^*1Σ^*1Σ^*, where |x| = |z| ≥ |y|}.

a. Show that C₁ is a CFL.

b. Show that C₂ is not a CFL.