Exam 2 Practice Questions


1.  Prove that the sum of two odd integers is an even integer.



2.  Prove that the product of any two odd integers is an odd integer.



3.  Is the following statement true or false?   ëxû + ëyû = ëx+yû  If it is true, prove it using a direct proof.  If it is false, prove it by counterexample.



4.  Prove the following statement by weak mathematical induction:
       1     +   1     + …. +    1       =    n   ,  for all integers n ³ 1
     1*2      2*3               n(n+1)      n+1



5.  Prove that n3 + n is even for all integers n



6.  Prove that 3(½ n2 + ½ n + 2) divisible by 3, for all integers n