Practice Tutorial 3 (21.1.2) - Lecture -20 - Discrete Mathematics

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6 sample questions

Question 1.
Is {2} a subset of {1, 2, 3}?
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Check if all elements of the first set are in the second set.
Question 2.
What is the definition of a symmetric relation?
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Consider the pairs involved in a symmetric relation.
3Question 3.
If (A ∩ C) ⊆ (B ∩ C), can we conclude A ⊆ B?
- True
- False
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Think about how intersections dictate membership.
4Question 4.
Does an anti-symmetric relation allow both (a, b) and (b, a) if a ≠ b?
- True
- False
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Recall the definition carefully.
Question 5.
Demonstrate with a concrete example how a relation can be both symmetric and irreflexive.
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Ensure no self-pairs are included for irreflexivity.
Question 6.
Create a scenario where a non-empty set contains both reflexive and irreflexive relations, detailing how this is possible.
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Reflect on the definitions carefully for overlaps.

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