Lecture 6 - Equivalence Relations Flashcards

1
Q

What is an equivalence relation?

A

A relation on a set that is reflexive, symmetric and transitive.

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2
Q

What does an equivalence relation look like in a digraph?

A

Loops on all elements, directed edges from each vertex to each other vertex, in both directions.

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3
Q

By looking at a matrix, how can you tell if the relation it represents is reflexive?

A

There are 1’s on the main diagonal.

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4
Q

By looking at a matrix, how can you tell if the relation it represents is symmetric?

A

The (i,j)th entry is equal to the (j, i)th entry.

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5
Q

By looking at a matrix, how can you tell if the relation it represents is transitive?

A

The (i,j)th entry of A * A is nonzero when the (i,j)th entry of A is nonzero.

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