Practice Definition Of Equivalence Relation (21.1)

Practise this section

8 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define equivalence relation.
Show hintHide hint
What are the three key properties?
Question 2.
Give an example of reflexivity.
Show hintHide hint
Think of an element relating to itself.
3Question 3.
What does reflexivity imply about the elements in a set?
- Each element is related to itself
- All elements are related to one another
- Elements relate in pairs
Show hintHide hint
Think about self-relation.
4Question 4.
If a is related to b and b is related to c, what can we say about a and c?
- True
- False
Show hintHide hint
Follow the chain of relations.
Question 5.
Prove that the relation R defined on integers by a R b if a - b is divisible by 5 is an equivalence relation.
Show hintHide hint
Use specific integers to illustrate your proof.
Question 6.
Given two equivalence classes [a] and [b], prove that if they intersect, they must be the same.
Show hintHide hint
Track the connections between shared elements.

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