A, B and C are subsets of the universal set U such that : \(U = {0, 1, 2, 3,..., 12}; A = {x : 0 \leq x \leq 7}; B = {4, 6, 8, 10, 12}; C = {1 < y < 8}\), where y is a prime number.

(a) Draw a venn diagram to illustrate the information given above;

(b) Find: (i) \((B \cup C)'\); (ii) \(A' \cap B \cap C\).

(a) Given that \(\log_{10} 2 = 0.3010, \log_{10} 7 = 0.8451\) and \(\log_{10} 5 = 0.6990\), evaluate without using logarithm tables:

(i) \(\log_{10} 35\); (ii) \(\log_{10} 2.8\).

(b) Given that \(N^{0.8942} = 2.8\), use your result in (a)(ii) to find the value of N.