SOLUTION: Show by contraposition that if n is an integer n³+5 is odd then n is even

Let P be  is odd

and Q be  is even



The problem asks to show P --> Q by showing ~Q --> ~P   (notice these are logically equivalent statements).  



"If it rains then the garden will be watered."  is logically equivalent to

"If the garden is not watered then it did not rain."



~Q means n is not even (i.e. n is odd)



1. Assume n is odd

2.  is odd (odd x odd is odd, so odd x odd x odd is also odd)

3.  is even  (odd + odd is even)

4.  ~Q --> ~P

5.  P --> Q