Practice Symmetry (22.5.2) - Lecture -22 - Discrete Mathematics

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6 sample questions

Question 1.
What is an equivalence relation?
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Think about the properties it needs to satisfy.
Question 2.
Provide a simple example of a partition.
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Make sure the subsets do not share any elements.
3Question 3.
What is the primary property that defines an equivalence relation?
- Only reflexivity
- All three properties: Reflexivity
- Symmetry
- Transitivity
- Only symmetry
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Consider what each property entails.
4Question 4.
True or False: A partition can include empty subsets.
- True
- False
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Think about the definition of a partition.
Question 5.
If set A = {1, 2, 3} and set B = {3, 4, 5}, create an equivalence relation that relates elements of A to elements of B.
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Consider how you might categorize elements across the two sets.
Question 6.
Given a set S = {x, y, z, w} and the partition {{x, y}, {z, w}}, formulate the equivalence relation and justify its reflexivity, symmetry, and transitivity.
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Revisit how to articulate properties based on pairs.

4 more questions in this section. Enroll free to practise them all.