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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.

Ишлатилган мисол · truth table of p implies q

Discrete-Math · Propositional-Logic

Truth table of p implies q

Қадамма-қадам

p \Rightarrow q
2 variable(s) → 4 rows. Fill in every combination.
\
Contingent: true for some inputs, false for others.

Жавобни кўрсатиш

p \Rightarrow q

Энди сизлар Мавзуни танланг, ёзинг ёки ўзингиз чизинг. Ҳар бир қадам, расм, жавоб сиз сўрагунча яширин.

Ўзингиз ишлашда давом этинг

Бепул ҳисоб ҳар бир дарсга ёзув қўшиб беради, сиз тугатган нарсалар ва ҳал қилинган масалалар бир жойда қайд этилади ва сиз бу саҳифа ҳақида устоздан сўрашингиз мумкин. Математика ўзида очиқ бўлиб, унга кириш ёки киришни истамаган ҳар кимга очиқ.

Ройхатдан ўтиш Кириш

Бу ерда қўлланилган белгилар

Барча белгилар учун тўлиқ таъриф, сурат ва ҳар бир ҳарфнинг маъносини кўриш учун белгини босинг.

Қандай: Relations, functions and equivalence

2 variable(s) → 4 rows. Fill in every combination.
Contingent: true for some inputs, false for others.

Одамлар сўрайдиган саволлар

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.

Кўпроқ Set Theory & Logic

Sets and operations Cardinality and infinity Logic and methods of proof