2)  Let Q(x,y) be the statement ``x has been a contestant on y''.  Express each of the following sentences in terms of Q(x,y) and quantifiers,  where the universe of discourse for x is the set of all students at Gustavus and the universe for y is the set of all quiz shows on television.
 

a)  There is a student at Gustavus who has been a contestant on a television quiz show.

b)  No student at Gustavus  has ever been a contestant on a television quiz show.

c)  Every television quiz show has had a student from Gustavus as a contestant.

d)  At least two students from Gustavus have been contestants on Jeopardy.

Express the following in English.
 

e)  {universal quantifier} y {universal quantifier}x Q(x,y)

f)  {universal quantifier} x {existential quantifier} y Q(x,y)

3)  Grimaldi 2.5:  6,16

4)  Prove that if x and y are real numbers, then max(x,y) + min(x,y) = x+y.
(Hint:  Use a proof by cases, with the two cases corresponding to x >= y and x <y, respectively.)