Practice Lecture -20 (21.1.1) - Lecture -20 - Discrete Mathematics

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6 sample questions

Question 1.
Prove that if A ∩ C ⊆ B ∩ C, then A ⊆ B.
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Use the definition of subset and intersect sets.
Question 2.
Define a symmetric relation.
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Think about how pairs can interrelate in a set.
3Question 3.
What does it mean for A ∩ C ⊆ B ∩ C?
- A ⊆ B
- A ∩ B ⊆ C
- C is empty
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Think of the implications of the filter analogy we discussed.
4Question 4.
True or False: In a symmetric relation, missing (a,b) implies that (b,a) is also not present.
- True
- False
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Revisit the definition of symmetry.
Question 5.
Can there exist a relation on a set with no overlap, yet be both symmetric and irreflexive? Justify your answer.
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Contrast the definitions to guide your reasoning.
Question 6.
Create a relation matrix for 3 elements that exemplifies a reflexive yet symmetric relation.
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Remember to ensure all ordered pairs considered satisfy the properties discussed.

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