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tux
Discrete math Prove directly For n∈N, if n is odd, then 3n+1 is even For x,y∈R, if x and y are rational, then x+2y is rational Prove by contrapositive For n ∈N if n^3 is odd, then n is odd
first one.. n is odd so it can be written as 2k+1 3n+1 = 3(2k+1) +1 = 6k +4 = 2(3k+2) and this is even for any k
contrapositive: n=2k (2k)^3=8k^3=2*(4k^3)