Over the universe of college students, let M(x) be "x is a math major", F(x) be "x is a freshman", and T(x) be "x has taken MATH. For each of the following English sentences, 

i) write as a formula, ii) write the negation of the formula, and iii) write each negation as an English sentence. Remember to write universally quantified statements as IMPLICATIONS.

 

a) There is a math major who has not taken MATH.

b) All math majors have taken MATH or are freshman.