Find the union and intersection of each of the following families or indexed collections:
(a) Let β = {{1, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {4, 5, 6, 7, 8}}.
(b) Let β = {{1, 3, 5}, {2, 4, 6}, {7, 9, 11, 13}, {8, 10, 12}}.
(c) For each natural number n, let Aβ = {5n, 5n + 1, 5n + 2 ..., 6n}, and let β = {Aβ: n β β}.
(d) For each natural number n, let Bβ = β β {1, 2, 3, ..., n} and let β’ = {Bβ: n β β}.
(e) Let β be the set of all sets of integers that contain 10.
(f) Let Aβ = {1}, Aβ = {2, 3}, Aβ = {3, 4, 5}, ..., Aββ = {10, 11, ..., 19}, and let β = {Aβ: n β {1, 2, 3, ..., 10}}.
(g) For each natural number n, let Aβ = (0, 1/n), and let β = {Aβ: n β β}.
(h) For r β (0, β), let Aα³ = [βΟ, r), and let β = {Aα³: r β (0, β)}.
(i) For each real number r, let Aα³ = [|r|, 2|r| + 1], and let β = {Aα³: r β β}.
(j) For each n β β, let Mβ = {..., β3n, β2n, βn, 0, n, 2n, 3n, ...}, and let β³ = {Mβ: n β β}.
(k) For each natural number n β₯ 3, let Aβ = [1/n, 2 + 1/n] and β = {Aβ: n β₯ 3}.
(l) For each n β β€, let Cβ = [n, n + 1) and let α = {Cβ: n β β€}.
(m) For each n β β€, let Aβ = (n, n + 1) and β = {Aβ: n β β€}.
(n) For each n β β€, let Dβ = (βn, 1/n) and β© = {Dβ: n β β}.
(o) For each prime number p, let pβ = {np: n β β} and β be the family {pβ: n β β and p is prime}.
(p) For each n β β€, let Tβ = {(x, y) β β Γ β: 0 β€ x β€ 1, 0 β€ y β€ xβΏ} and β = {Tβ: n β β}.
(q) For each n β β€, let Vβ = {(x, y) β β Γ β: 0 β€ x β€ 1, xβΏ β€ y β€ nβββ x} and β = {Vβ: n β β}.