Express the following statements using logic symbols such as ",,,,,and,or", etc. Form the negation of the formal statements, and re-express in plain English.

a) For all elements there exists an element such that for all with , =1 implies 1

[Here ,, are elements of some field.]

b) The angle sum in every hyperbolic octagon is greater than

c) All flavors of quarks have the same charge and the same mass.

d) Every student in this class who does all the homework assignments and attends all the lectures will score at least 50 percent on the final exam.