Practice question · Select all that apply
Let R be 'has the same parity as' on {1, 2, 3, 4}. Select every pair that belongs to R.
Hints
- Two numbers are related when both are even or both are odd.
- Do not forget that every element is related to itself.
Show the answer
- B. (2, 4)
- D. (1, 3)
- E. (3, 3)
Why
(1,3) are both odd, (2,4) both even, and (3,3) is reflexive. (1,2) and (4,1) mix an odd with an even, so they are excluded. The relation splits the set into {1,3} and {2,4}, its two equivalence classes.
Practise Relations and Equivalence
The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Relations and Equivalence
- Complete the definition of transitivity.
- "Has the same remainder mod 3" partitions the integers into three classes. Why is the quotient construction,…
- Order the steps that verify 'has the same parity as' is an equivalence relation.
- An equivalence relation partitions its set into classes with no overlaps and nothing left out. Why do…
- Every function is a relation.
- An equivalence relation is reflexive, symmetric AND transitive. Sort each relation.
- The relation 'has the same remainder when divided by 3' partitions the integers into equivalence classes. How…