CPSC 121 Lecture Notes - Lecture 25: Prime Number
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Cpsc 121 lecture #25 transformations and the challenge method. Topics included: direct proofs, with existential quantifiers + examples, with universal quantifiers + examples. Direct proofs: existential: x d, p(x, 1) choose an x where p(x) is true, 2) show that p(x) is true, ex. It is prime (optional explanation: because its only factors are 1 and 5): now 35+2 is 245 which is divisible by 5, hence 35+2 is not prime, qed, example: There are perfect squares and perfect cubes larger than 1 that are also fibonacci numbers (source: belleville, lecture 25 proof. It is a perfect square because it is the product of 12 x 12: now fib(144), 144 is a fibonacci number and a perfect square, choose x = 8. It is a perfect cube because it is the product of 2 x 2 x 2: now fib(8), 8 is a fibonacci number and a perfect square, qed, universal: x d, p(x)
