Explain peano''s axioms with suitable example, Mathematics

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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

x'Λ y
(x' Λ y ) ν (x' Λ y')

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