Practice question · True or false
Every function is a relation.
Hints
- A function can be recorded as the set of pairs (input, output).
- The converse is the interesting question.
Show the answer
True
Why
True. A function is a relation with the extra restriction that each domain element appears in exactly one pair. The converse fails: 'differs by 1' relates 3 to both 2 and 4, so it is a relation but not a function.
Practise Relations and Equivalence
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More questions on Relations and Equivalence
- Complete the definition of transitivity.
- Let R be 'has the same parity as' on {1, 2, 3, 4}. Select every pair that belongs to R.
- "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…
- 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…