1. Induction and prime factorisation of natural numbers: Let n EN be a natural number. A prime factorisation of n is an equation n = pi'p2 prime number and d; E {0}UN. Using MMathematical Induction, prove that every natural number has a prime factorisation. de ..P*, where for i = 1,..., k, Pi is a The following statements inay be useful in your proof: (Q1) Vm, n € N (m < < n) = 1 <1: m (Q2) Vm, n E N (m and n have prime factorisations) (mn has a prinie factorisation): (Q3) Vn E N (n > 2) =

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.