A: Proof

Question 1

Proof by deduction

Answer 1

Use algebra to come to a conclusion

Question 2

Proof by exhaustion

Answer 2

Check every possible case

Question 3

Disproof by counter example

Answer 3

Find just one case where the conjecture is invalid

Question 4

Proof by condtradiction

Answer 4

Assume the opposite of the conjecture

Question 5

Proof of infinity of primes

Answer 5

• Assume finite set of primes
• Let the set be P = P1 x P2 x P3 … x Pn where P is the product of all primes
• Consider N where N = P + 1
• Case 1: N is prime
• N has a factor that is a prime that is bigger than any other prime and not in the set which contradicts the assumption that P is the product of all primes
• Case 2: N is not prime
• N has prime factors as it is not prime
• N does not have any primes in the set P as they will all divide with remainder 1
• N must be divisible by some other prime which contradicts the assumption that P is the product of all primes
• CONTRADICTION therefore assumption is wrong and there are an infinite number of primes