Exercise 1. (a) Prove (using direct proof) that Vn € {odd integers}, 3j € Z|n = 2j - 1. (b) Write the statement The sum of the first n odd natural numbers is n² 2 using summation notation and the alternative definition of odd proven above. (c) Use the Principle of Mathematical Induction to prove that the sum of the first n odd natural numbers is n².

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