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Practice Problemon set operations


Consider the following sets:

$ \begin{align} S_1 &= \left\{ \frac{1}{2}, 1, 1.4, 2 \right\}, \\ S_2 & = \left\{ 0.\bar{9}, 1.40, \frac{42}{21}, 17\right\}. \\ \end{align} $

Write $ S_1 \cup S_2 $ explicitely. Is $ S_1 \cup S_2 $ a set?


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Answer 1

All elements in the following union are distinct, therefore the union is a set.

$ S_1 \cup S_2 = \{ \frac{1}{2}, 0.\bar{9}, 1, 1.4, 2, 17 \} $

Lecture 3.PNG ($ S_1 \cup S_2 $ represented by colored region.)


Answer 2

Write it here.


Answer 3

Write it here.


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