A language L 1 is smaller than another language L 2 if L 1 L 2 and L 1 L 2 Let T be any language closed under concatenation that is, if t 1 T and t 2 T then t 1 t 2 is also an element of T Show that if T contains S but T S , then S is smaller than T We can summarize this by saying that S is the sma...

Answer and Explanation Assume that T contains S but ...

A language L 1 is smaller than another language L 2 if L 1 L 2

Question:

A language L₁ is smaller than another language L₂ if L₁ ⊂ L₂ and L₁ ≠ L₂• Let T be any language closed under concatenation; that is, if t₁ ∈ T and t₂ ∈ T. then t₁ t₂ is also an element of T. Show that if T contains S but T ≠ S*, then S* is smaller than T. We can summarize this by saying that S* is the smallest closed language containing S.