abel the following statement as True (T) or False (F): Let L be any Turing recognizable language. Then L is Turing recognizable.

Exercise 5-6 Prove that the following sentences are theorems. please help with 1,5,7,9 (1) A ⊃ (A ∨ B) (5)(A ∨ B) ⊃ [C ⊃ (A ∨ B)] (7) (A ∨ B) ⊃ [(A ⊃ B) ∨ (B ⊃ A)] (9) (A ⊃ B) ≡ (∼ B ⊃ ∼ A)

1) What is the following recursive set S? • 3 ∈ S • x,y ∈ S → (x + y) ∈ S 2)  Consider the following recursive set S ⊂Z×Z. Give an example of a pair of integers a,b that is not in the set S. • (3,5) ∈ S • (x,y) ∈ S → (x + 2,y) ∈ S • (x,y) ∈ S → (y,x) ∈ S • (x,y) ∈ S → (−x,y) ∈ S

hello by Peter Linz, "Introduction to Formal Languages and Automaton", 6th edition, 2017. The cut is from chapter 2, section 1. thanks:))