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Relations, functions and equivalence
Relations as sets of pairs; reflexive, symmetric, transitive; functions and bijections.
A relation is a set of ordered pairs; an equivalence relation (reflexive, symmetric, transitive) partitions its set into classes; a function is a relation with exactly one output per input. Picture it: "same remainder mod 3" splits the integers into three columns. Think it: a bijection is how we say two sets have the same size, including infinite ones.
Umzekelo osebenzelayo · truth table of p implies q
Truth table of p implies q
Inyathelo ngenyathelo
- p \Rightarrow q
2 variable(s) → 4 rows. Fill in every combination.
- \
Contingent: true for some inputs, false for others.
Bonisa impendulo
ngoku Khetha ingxaki, okanye ubhale okanye uzobe yakho. Inyathelo ngalinye, umfanekiso, impendulo ifihlakele de ubuze.
I akhawunti ekhululekileyo idibanisa amaphetshana kwi ncwadi nganye, irekhodi lento ogqibe ngayo, iingxaki zakho ezisoliweyo kwindawo enye, nomfundi onokuthi ubuze malunga nale phepha. IiMathematiki ngokwazo zivuliwe kubo bonke, bangeniswe okanye hayi.
Bhalisa Igama elithileIimpawu ezisetyenziswa apha
Nqakraza nasiphi na isibonakaliso sokuqonda okupheleleyo, umfanekiso, nokuba iileta zonke zithetha ntoni.
Indlela yokusebenza: Relations, functions and equivalence
- 2 variable(s) → 4 rows. Fill in every combination.
- Contingent: true for some inputs, false for others.
Imibuzo abantu bebuza
Are some infinities bigger than others?
Yes. The integers and the rationals can be listed; the real numbers cannot (Cantor's diagonal argument), so there are strictly more reals than integers.
What is the difference between a relation and a function?
A relation pairs inputs with outputs freely; a function is a relation in which every input gets exactly one output.
IiNkqubo Set Theory & Logic
Sets and operationsCardinality and infinityLogic and methods of proof