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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Prove that if A ∩ C ⊆ B ∩ C, then A ⊆ B.
💡 Hint: Use the definition of subset and intersect sets.
Question 2
Easy
Define a symmetric relation.
💡 Hint: Think about how pairs can interrelate in a set.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does it mean for A ∩ C ⊆ B ∩ C?
- A ⊆ B
- A ∩ B ⊆ C
- C is empty
💡 Hint: Think of the implications of the filter analogy we discussed.
Question 2
True or False: In a symmetric relation, missing (a,b) implies that (b,a) is also not present.
- True
- False
💡 Hint: Revisit the definition of symmetry.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Can there exist a relation on a set with no overlap, yet be both symmetric and irreflexive? Justify your answer.
💡 Hint: Contrast the definitions to guide your reasoning.
Question 2
Create a relation matrix for 3 elements that exemplifies a reflexive yet symmetric relation.
💡 Hint: Remember to ensure all ordered pairs considered satisfy the properties discussed.
Challenge and get performance evaluation