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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).

Gewerkte voorbeeld · {1,2,3,4} union {3,4,5,6}

Set-Theory · Sets

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

Stap met stap

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

    The two sets.

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

    Keep everything in either set.

  3. |A| = 4,\ |B| = 4,\ |A \cup B| = 6

    Cardinalities. Note |A ∪ B| = |A| + |B| − |A ∩ B|.

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

Nou jy Kies'n probleem, of tik of teken jou eie.'n Foto, die antwoord wat verberg is totdat jy vra.

Hou jou eie werk

'n Vry rekening voeg notas by oor elke les, 'n verslag van wat jy klaar gemaak het, jou opgelos probleme op een plek, en' n tugmeester wat jy kan vra oor hierdie bladsy. Die wiskunde self is oop vir almal, geteken in of nie.

Meld op Meld aan

Simbools wat hier gebruik word

Maak enige simbool van die volledige definisie,'n prent en wat elke letter daarin beteken.

Hoe om: Sets and operations

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

Vrae wat mense vra

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.

Meer in Set Theory & Logic

Relations, functions and equivalenceCardinality and infinityLogic and methods of proof