Description of the language generated by grammar

Question

Question 1: Use mathematical induction prove that:

Question 2: Show that √3 is irrational (use contradiction to prove)

Question 3: Show that if S₁ and S₂ are definite sets with |S₁|= n and |S₂|= m, then:

S₁ U S₂ |≤ n + m

Question 4: Give a simple description of the language generated by the grammar with productions:

S → αA

A → bS

S → λ

Question 5: Explain the meaning of figure shown below which represents a binary adder.

Figure: Binary adder state transformation