1) There is an astronomer who is not nearsighted. Everyone who wears glasses is nearsighted. Furthermore, everyone either wears glasses or wears contact lenses. Therefore, some astronomer wears contact lenses.

a) Use the predicate symbols: A(x), N(x), G(x), C(x) to write the above statements as a wff argument.

b) Using predicate logic, prove that the argument is valid.

2) Complete the following exhaustive proof of:

If a positive integer x is less than 10, then x2 < 200.

List positive integers x < 10 List corresponding x2 Is x2 < 200?

   

   

   

   

   

   

   

   

   
3) Use a direct proof to show:

"If x is an odd integer and y is an even integer, then x + y is odd."

4) Use proof by contraposition to show:

"If x2 is even, then x is even."

5) Use proof by contradiction to show:

"If x2 is even, then x is even."