**Writing Formal Negations
To Universal Conditional Statements**

**ANSWERS**

- students
's GPA is better than 3.5*x | x*(*~*studies a lot.)*x*

There are some students whose GPA's are better than 3.5 and they don't study a lot.

- polygons
|*p*has 3 sides ~(*p*is a triangle)*p*

There exists a polygon such that the polygon has 3 sides and it is not a triangle.

- numbers
|*n*is real*n*(*~**n*^{2}is positive.)

There are some numberssuch that*n*is real and*n**n*^{2}is not positive.

- girls
|*g*dates that guy and ~(*g*is crazy)*g*

There are some girls who date that guy and who are not crazy.