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Question 4
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Without using tables or calculator, evaluate:
log10( ) – 2log10( ) + log10( ).
- Given that X ={x : 10 ≤ x< 15} and Y = {even numbers < 18} are subsets of U = {10, 11, 12, …, 20}, find:
- X
 Y;
- n(X’
 Y).
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The Chief Examiner reported that this question was attempted by majority of the candidates and they performed well in it.
In part (a), candidates were reported to apply the laws of logarithms correctly. They were able to express the given problem as a single logarithm
i.e. log10( ) – 2log10( ) + log10( ) = log10( ) = log10( ) = log10( ) = log1010 = 1.
In part (b), majority were reported to have obtained the elements of sets X and Y as X = {10, 11, 12, 13, 14} and Y = {10, 12, 14, 16}. X  Y = {10, 12, 14}.
X’ = {15, 16, 17, 18, 19, 20}. X’  Y = {16}. Therefore, n(X’  Y) = 1.
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