Writing Formal Negations To Universal Conditional Statements



  1. students x | x's GPA is better than 3.5 ~(x studies a lot.)
    There are some students whose GPA's are better than 3.5 and they don't study a lot.

  2. polygons p | p has 3 sides ~(p is a triangle)
    There exists a polygon such that the polygon has 3 sides and it is not a triangle.

  3. numbers n | n is real ~(n2 is positive.)
    There are some numbers n such that n is real and n2 is not positive.

  4. girls g | g dates that guy and ~(g is crazy)
    There are some girls who date that guy and who are not crazy.