For the following statements prove using exhaustion direct c

For the following statements, prove using exhaustion, direct, contrapositive, or contradiction. Use the method that makes the most sense. Statement: There is no largest integer Statement: If 8x - 1 is even, then X is even Statement: If n is even, then n^3 is even

Solution

4)

Assume there is a largest integer say N

But if N is integer so is N+1

Hence N+1 is larger than N which is a contradiction

Hence, there is no largest integer

5)

False

Let, x=2

8*2-1=15 which is odd

6)

True

n is even so n=2k for some integer k

n^3=8k^3 which si even as it is multiple of 2