Practice Transitive Closure (18.7.3) - Operations on Relations - Discrete Mathematics - Vol 1

Practice: Transitive Closure

Lesson 18.7.3Operations on Relations

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9 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the transitive closure of the relation R = {(1, 2), (2, 3)}?
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Think of the pairs that need to be added to ensure transitivity.
Question 2.
Which property must be satisfied for a relation to be a transitive closure?
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If A is related to B and B is related to C, what must also be true?
3Question 3.
What is the transitive closure of a relation?
- A set containing direct pairs
- The smallest superset satisfying transitive properties
- A completely arbitrary set
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Remember the goal is to ensure A relates to C if A relates to B and B to C.
4Question 4.
True or False: The transitive closure can be computed in a single step.
- True
- False
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Think back to our example!
Question 5.
You have a relation R = {(1, 2), (2, 3), (4, 5)}. Find R's transitive closure and explain the steps taken.
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Look at pairs and see if they indirectly relate to each other.
Question 6.
Given the relation R = {(a, b), (b, c), (c, d), (d, a)}, calculate its transitive closure.
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Consider how far each node can reach through others.

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