I'm in math proof and problem solving and would like someone to tell me if I am on track with these answers. The question is:
Are these statements true or false? The universe of discourse is the set of all people, and T(x, y) means “x and y are twins.” Explain how you determined your solution.
a. ∀x ¬T(x, x) True: For all people there is not a situation where x and x are twins.
b. ∃y T(y, y) False: There exists a y where y and y are twins.
c. ∃x ∀y T(x, y) True: There exists an x that for all y's, x and y are twins.
d. ∀x ¬∃y T(x, y) False: For all x's there does not exist a y where x and y are twins.
e. ∃x ¬∃y T(x, y) True: There exists an x where there is not a y where x and y are twins.
f. ∀x ¬∀y T(x, y) False: For all x's and not for all y's, x and y are twins.