1)
Assume n is not even. Set n=2k+1 where k is a natural number
Show that the assumption is false because n^3 +5 cannot be even when n=2k+1.
2)
Let
Show that 1/x can be written as a quotient.
Been stuck on these two for a while now. Would anyone be able to help me with them? Thanks!
#1.) Prove by contradiction that for all n ∈ Z, if n^3 + 5 is odd, then n is even
#2.) Prove using a direct proof that for every rational number x, if x ≠ 0, then 1/x is rational