1. Induction and prime factorisation of natural numbers: Let n EN be a natural number. A prime factorisation of n is an equation n = p'p...p , where for i = 1,... , k, pi is a prime number and d; E {0}UN. Using Mathematical Induction, prove that every natural number has a prime factorisation. di, d2 de The following statements inay be useful in your proof: (Q1) Vm, n €N (m < n) = < : (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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Q: 1. Induction and prime factorisation of natural numbers: Let n EN be a natural number. A prime…

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Statements and Logic

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