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Find \( n(A) \) for the set \( A = \left\{ \frac{1}{3}, \frac{2}{4}, \frac{3}{5}, \frac{4}{6}, \ldots, \frac{17}{19}, \frac{18}{20} \right\} \).

Answer :

The set A contains 18 fractions where both the numerator and the denominator are increasing by 1 in each subsequent fraction.

The number of elements in a set notation. The set A = {(1)/(3),(2)/(4),(3)/(5),(4)/(6),...,(17)/(19),(18)/(20)} contains fractions where both the numerator and the denominator are increasing by 1 in each subsequent fraction. The starting fraction is (1/3) and the ending fraction is (18/20), there will be 18 fractions, so the number of elements, n(A), in set A is 18.

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