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Mathematics, 30.09.2019 22:00 hinacat87
Put the following statements into order to prove that if 3n+4 is even then n is even. put n next to the 3 statements that should not be used.1. then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1.2. by definition of odd, there exists integer k such that n=2k+1.3. thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, .4. therefore, by definition of odd, 3n+4 is odd.5. since k is an integer, t =3k+3 is also an integer.6. thus, there exists an integer t such that 3n+4=2t+1.7. suppose n is odd.8. thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, .9. suppose 3n+4 is even.10. by definition of odd, n=2k+1.
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