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

Practice - Transitive Closure

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Practice Questions

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Question 1 Easy

What is the transitive closure of the relation R = {(1, 2), (2, 3)}?

💡 Hint: Think of the pairs that need to be added to ensure transitivity.

Question 2 Easy

Which property must be satisfied for a relation to be a transitive closure?

💡 Hint: If A is related to B and B is related to C, what must also be true?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the transitive closure of a relation?

A set containing direct pairs
The smallest superset satisfying transitive properties
A completely arbitrary set

💡 Hint: Remember the goal is to ensure A relates to C if A relates to B and B to C.

Question 2

True or False: The transitive closure can be computed in a single step.

True
False

💡 Hint: Think back to our example!

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

You have a relation R = {(1, 2), (2, 3), (4, 5)}. Find R's transitive closure and explain the steps taken.

💡 Hint: Look at pairs and see if they indirectly relate to each other.

Challenge 2 Hard

Given the relation R = {(a, b), (b, c), (c, d), (d, a)}, calculate its transitive closure.

💡 Hint: Consider how far each node can reach through others.

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