(a) Copy and complete the following table for multiplication modulo 11.

\(\otimes\) 1 5 9 10
1 1 5 9 10
5 5      
9 9      
10 10      

Use the table to : (i) evaluate \((9 \otimes 5) \otimes (10 \otimes 10)\);

(ii) find the truth set of :(1) \(10 \otimes m = 2\);  (2) \(n \otimes n = 4\)

(b) When a fraction is reduced to its lowest term, it is equal to \(\frac{3}{4}\). The numerator of the fraction when doubled would be 34 greater than the denominator. Find the fraction.

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