Solution for Section 2.1 Question 5

5.  Let F(x) be the predicate "4 is a factor of x" and let T(x) be the predicate "2 is a factor of x".

The statement can be written symbolically as: " x Z, F(x) T(x).

Now recall that the negation of "" x D,  if  P(x)  then S(x)'' is $ x D such that P(x) L ~S(x).

The negation of the given statement is  $ x Z such that F(x) L ~T(x). In English this would be: There is an integer which has a factor of 4 but not a factor of 2. The original statement is true.

Back to Section 2.1