(a) A = {m, a, p, e}; B = {a, e, i, o, u} ; C = {l, m, n, o, p, q, r, s, t, u}
(i) \(A \cup B = {a, e, i, m, o, p, u}\)
(ii) \(A \cup C = {a, e, l, m, n, o, p, q, r, s, t, u}\)
(iii) \(A \cup (B \cap C)\)
\(B \cap C = {o, u}\)
\(A \cup (B \cap C) = {m, a, p, e, o, u}\)

Biology students = n(B) = 190
Chemistry students = n(A) = 300
Let \(n(A \cap B) = a\)
(i) From the Venn diagram,
\((300 - a) + a + (190 - a) + 70 = 400\)
\(560 - a = 400 \implies a = 160\)
\(\therefore\) 160 students offer both Biology and Chemistry.
(ii) Students offering at least one of Biology and Chemistry
= \(n(A) + n(B) + n(A \cap B)\)
= \((300 - 160) + (190 - 160) + 160\)
= \(140 + 30 + 160\)
= 330 students
330 students offer at least one of Biology and Chemistry.