(a) Evaluate without using the mathematical table or calculator, (log_{10} sqrt{30} – log_{10} sqrt{6} + log_{10} sqrt{2}).
(b)
(U = {1, 2, 3, …, 10} ; A = {1, 2, 3, 4, 5} ; B = {2, 3, 5}) and (C = {6, 8, 10}). (i) Given that the Venn diagram represents the sets above, copy and fill in the elements.
(ii) Find (A cap C) ; (iii) Find (A cap B’).
Explanation
(a) (log_{10} sqrt{30} – log_{10} sqrt{6} + log_{10} sqrt{2})
= (log_{10} (sqrt{frac{30}{6}} times sqrt{2}))
= (log_{10} (sqrt{5} times sqrt{2}))
= (log_{10} sqrt{10})
= (log_{10} (10^{frac{1}{2}}))
= (frac{1}{2} log_{10} 10)
= (frac{1}{2}).
(b)
(ii) (A cap C = { } )
(iii) (A cap B’ = {1, 4}).