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

  1. x'Λ y
  2. (x' Λ y ) ν (x' Λ y')

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sin(x)+cos(x)

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