Practice Part B: Symmetric, Anti-symmetric And Irreflexive Relations (21.5.2)

Practise this section

9 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
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a symmetric relation in your own words.
Show hintHide hint
Think about how relationships often work in pairs.
Question 2.
What is an example of an irreflexive relation?
Show hintHide hint
Consider numerical comparisons where one number can’t equal itself.
3Question 3.
What defines a symmetric relation?
- If (a
- b) implies (b
- a)
- If (a
- b) implies b > a
- If (a
- b) implies (a
- a)
Show hintHide hint
What would happen if you reversed the pairs in a relationship?
4Question 4.
True or False: An anti-symmetric relation can have (a, a) and (b, b) without issue.
- True
- False
Show hintHide hint
Consider the definition of anti-symmetry carefully.
Question 5.
Given a set A = {a, b, c}, construct all possible relations and categorize them by symmetry, anti-symmetry, and irreflexivity.
Show hintHide hint
Use the definition of each type to guide your categorization.
Question 6.
Prove that a symmetric relation on a set can never be irreflexive.
Show hintHide hint
Start with the definitions of symmetric and irreflexive relations.

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