Question
1.Suppose you wish to prove a theorem of the form if (n is even) then ( n 2 is even). a) If you give a
1.Suppose you wish to prove a theorem of the form if (n is even) then (n2 is even). a) If you give a direct proof, what do you assume and what do you prove? b) If you give an indirect proof, what do you assume and what do you prove? c) If you give a proof by contradiction, what do you assume and what do you prove?
2.Prove that the following is true for all positive integers n: n is even if and only if 5n2 + 4 is even.
3.What is the rule of inference used in the following? I can answer all the exercises, or I didnt work all night on this homework. I cannot answer all the exercises. Therefore, I didnt work all night on this homework.
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