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Sets and operations

Membership, subsets, union, intersection, complement, and Venn diagrams.

A set is a collection; the operations combine them: union (either), intersection (both), difference, complement. Picture it: a Venn diagram; each region is a combination of memberships. Think it: the operations satisfy the same laws as and/or/not, sets and logic are the same algebra (Boolean algebra).

Ýüklenen mysal · {1,2,3,4} union {3,4,5,6}

Set-Theory · Sets

{1,2,3,4} union {3,4,5,6}

Adım adım

A = \left\{1, 2, 3, 4\right\},\quad B = \left\{3, 4, 5, 6\right\}
The two sets.
A \cup B = \left\{1, 2, 3, 4, 5, 6\right\}
Keep everything in either set.
|A| = 4,\ |B| = 4,\ |A \cup B| = 6
Cardinalities. Note |A ∪ B| = |A| + |B| − |A ∩ B|.

Jawaby görkez

A \cup B = \left\{1, 2, 3, 4, 5, 6\right\}

Indi sen Bir meseläni saýla, ýa-da ýaz ýa-da özüňi surata çek. Her ädim, bir resim, jogap sorag berlençä gizlenýär.

Özüň işle

Mugt hasap her bir ders üçin notlar goşýar, tamamlanan zadyňyzyň ýazgysyny, çözen problemaňyzy bir ýerde, we bu sahypa barada sorap biljek mugallymy. Matematika özüçe her kim üçin açyk, girseň ýa girmeseň.

_Gün _Giriş

Şu ýerde ulanylan simwollar

Eň täze düşündirme, surat, we her harpyň manysy üçin her bir simwoly basyň.

Nädip: Sets and operations

Write each set explicitly, or describe it by a property.
For a union keep everything in either; for an intersection only what is in both.
Check |A ∪ B| = |A| + |B| − |A ∩ B|.

Adamlar soraýan soraglar

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.

_Ýaşa Set Theory & Logic

Relations, functions and equivalence Cardinality and infinity Logic and methods of proof