Let f, g, h denote the following closed binary operations on P(Z+). For A, B Z+,

Question:

Let f, g, h denote the following closed binary operations on P(Z+). For A, B ⊂ Z+, f(A, B) = A ∩ B, g(A, B) = A∪ B, h(A, B) = A△B.
a) Are any of the functions one-to-one?
b) Are any of f, g, and h onto functions?
c) Is any one of the given functions invertible?
d) Are any of the following sets infinite?
(1) f-1(ϕ)
(2) g-1(ϕ)
(3) h-1(ϕ)
(4) f-1{1})
(5) g-1({2})
(6) h-1({3})
(7) f-1({4, 7})
(8) g-'aS, 12})
(9) /i-1({5,9})