question 1 explain peanos axioms with suitable

Question

Question 1 Explain Peano's Axioms with suitable example

Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b²+1. Find

• a) (f °g)

• b) f^-1 and g^-1

Question 3 Let a, b, c be the elements in a lattice (A, ≤). Show that

• aν(bΛc) ≤(aνb)Λ(aΛc)
• (aΛb)ν(aΛc) ≤ aΛ(bνc)s

Question 4 Explain travelling Salesman problem with an example

Question 5 Express the following functions into conjunctive normal forms

1. x'Λ y
2. (x' Λ y ) ν (x' Λ y')