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

Instructor's note: This is really the second answer presented. It would be better if we could keep the first answer "as is", and put the correction as a second answer. Mistakes are nothing to be ashamed of! Making mistakes makes you learn! -pm

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

$ S_1 \cup S_2 = \{ \frac{1}{2}, 1, 1.4, 2, 17 \} $

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

WOW! That's a VERY nicely written answer. Great work. You only missed one little (somewhat tricky) detail. Can you guess what it is? MATH MAJORS: Can you help him? -pm

Okay, answer above edited to account for the following:

$ \frac{1}{9} = 0.\bar{1} $

$ \frac{1}{9} * 9 = 0.\bar{9} $

$ \frac{1}{9} * 9 = 1 $

$ \therefore 0.\bar{9} = 1 $

Instructor's comment: There you go! -pm

Answer 2

The union of S1 and S2 is all the elements in the Venn diagram: in S1, S2, and in both S1 and S2.

Answer 3

Write it here.

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