4. for each of the following statements, answer true or false and prove that your answer is correct. (a) (10 points) if a language l ⚆ {0, 1} ∗ is decidable, then every language l 0 ⚆ l is decidable. (b) (10 points) if f : {0, 1} ∗ → z is an upper semi-computable function, then the function g : {0, 1} ∗ → z given by g(x) = 2 − f(x) is lower semi-computable. (c) (10 points) the language {x ∈ {0, 1} ∗ : c(x) > |x|/3} is co-c. e. (d) (10 points) every language l ⚆ {0, 1} ∗ is either c. e. or co-c. e. or both.