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| − | [[ | + | = [[:Category:Problem solving|Practice Problemon]] set operations = |
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| − | Consider the following sets: | + | |
| + | Consider the following sets: | ||
<math> | <math> | ||
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S_2 & = \left\{ \sin (\frac{t}{2}), \sin (t+\frac{\pi}{2})\right\}. \\ | S_2 & = \left\{ \sin (\frac{t}{2}), \sin (t+\frac{\pi}{2})\right\}. \\ | ||
\end{align} | \end{align} | ||
| − | </math> | + | </math> |
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| + | Write <math>S_1 \cup S_2</math> explicitely. Is <math>S_1 \cup S_2</math> a set? | ||
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| − | ==Share your answers below== | + | |
| − | You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too! | + | == Share your answers below == |
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| + | You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too! | ||
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| − | + | === Answer 1 === | |
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| − | = | + | No, because a set must have unique elements; sin(t+pi/2) is basically cos(t). The union of both sets is a set with elements from both S1 and S2. S1 U S2 = {sin(t),cos(t),sin(t/2)} |
| − | <math | + | === Answer 2 === |
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| + | <math>S_1 \cup S_2 = \left\{ \sin (t),\sin (\frac{t}{2}), \cos (t)\right\}</math> | ||
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| + | <math>S_1 \cup S_2</math> is a set because the union of two sets is the set of all distinct elements from those two sets. In this case because <math> \sin (t+\frac{\pi}{2}) </math> and <span class="texhtml">cos(''t'')</span> are part of the same equivalence class, we only need to include one of these elements in our union set. | ||
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| − | <span style="color:green"> Instructor's suggestion: Can anyone illustrate the answer using a Venn diagram? -pm </span> | + | |
| + | <span style="color:green"> Instructor's suggestion: Can anyone illustrate the answer using a Venn diagram? -pm </span> | ||
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| − | ===Answer 3=== | + | |
| − | + | === Answer 3 === | |
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| + | S1 is sub set of S2. In venn diagram, omega which is { real positvie numbers between [-1,1]} will be entire domain. S1 will be included in S2. omega[S2[S1[]]]. I am not sure how to write mathmatical expression in this page and venn diagram. | ||
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| − | [[ECE302|Back to ECE302]] | + | [[2013 Spring ECE 302 Boutin|Back to ECE302 Spring 2013 Prof. Boutin]] |
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| + | [[ECE302|Back to ECE302]] | ||
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| + | [[Category:ECE302]] [[Category:ECE302Spring2013Boutin]] [[Category:Problem_solving]] [[Category:Set]] | ||
Revision as of 18:03, 10 January 2013
Contents
Practice Problemon set operations
Consider the following sets:
$ \begin{align} S_1 &= \left\{ \sin (t), \cos (t)\right\}, \\ S_2 & = \left\{ \sin (\frac{t}{2}), \sin (t+\frac{\pi}{2})\right\}. \\ \end{align} $
Write $ S_1 \cup S_2 $ explicitely. Is $ S_1 \cup S_2 $ a set?
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
No, because a set must have unique elements; sin(t+pi/2) is basically cos(t). The union of both sets is a set with elements from both S1 and S2. S1 U S2 = {sin(t),cos(t),sin(t/2)}
Answer 2
$ S_1 \cup S_2 = \left\{ \sin (t),\sin (\frac{t}{2}), \cos (t)\right\} $
$ S_1 \cup S_2 $ is a set because the union of two sets is the set of all distinct elements from those two sets. In this case because $ \sin (t+\frac{\pi}{2}) $ and cos(t) are part of the same equivalence class, we only need to include one of these elements in our union set.
Instructor's suggestion: Can anyone illustrate the answer using a Venn diagram? -pm
Answer 3
S1 is sub set of S2. In venn diagram, omega which is { real positvie numbers between [-1,1]} will be entire domain. S1 will be included in S2. omega[S2[S1[]]]. I am not sure how to write mathmatical expression in this page and venn diagram.
