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Exercise 11.11.22\newlineList all elements of the following sets:\newlinea. {1n∣n∈{3,4,5,6}}\left\{\frac{1}{n}\mid n \in \{3,4,5,6\}\right\}

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Q. Exercise 11.11.22\newlineList all elements of the following sets:\newlinea. {1n∣n∈{3,4,5,6}}\left\{\frac{1}{n}\mid n \in \{3,4,5,6\}\right\}
  1. Understand set notation: Understand the set notation.\newlineThe set notation {1n∣n∈{3,4,5,6}}\left\{\frac{1}{n} \mid n \in \{3,4,5,6\}\right\} means we are looking for a set of elements that are in the form of 1n\frac{1}{n}, where nn is an element of the set {3,4,5,6}\{3,4,5,6\}.
  2. List set elements: List the elements of the set 3,4,5,6{3,4,5,6}.\newlineThe elements of the set 3,4,5,6{3,4,5,6} are simply 33, 44, 55, and 66.
  3. Apply formula to elements: Apply the given formula (1)/(n)(1)/(n) to each element of the set {3,4,5,6}\{3,4,5,6\}. We will calculate (1)/(n)(1)/(n) for each value of nn in the set {3,4,5,6}\{3,4,5,6\}.
  4. Calculate (1)/(3)(1)/(3): Calculate (1)/(3)(1)/(3).(1)/(3)=1/3(1)/(3) = 1/3
  5. Calculate (1)/(4)(1)/(4): Calculate (1)/(4)(1)/(4).\newline(1)/(4)=1/4(1)/(4) = 1/4
  6. Calculate (1)/(5)(1)/(5): Calculate (1)/(5)(1)/(5).(1)/(5)=1/5(1)/(5) = 1/5
  7. Calculate (1)/(6)(1)/(6): Calculate (1)/(6)(1)/(6).\newline(1)/(6)=1/6(1)/(6) = 1/6
  8. List all calculated elements: List all the elements obtained from the calculations.\newlineThe elements obtained are 13\frac{1}{3}, 14\frac{1}{4}, 15\frac{1}{5}, and 16\frac{1}{6}.

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