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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).

ნამდვილი ასლი · {1,2,3,4} union {3,4,5,6}

Set-Theory · Sets

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

Step by step

  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|.

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

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უფასო ანგარიშის გამოყენებისას, ყველა გაკვეთილზე დამატებით ჩანაწერებს ნახავთ, დასრულებული და გადაწყვეტილი ამოცანების ჩანაწერებს ერთ ადგილას და მასწავლებელს, რომელსაც ამ გვერდის შესახებ შეკითხვა შეგიძლიათ გაუწიოთ. მათემატიკა ყველასთვის ხელმისაწვდომია, ანგარიშის შექმნის შემდეგაც კი.

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როგორ: 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|.

Questions people ask

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.

მეტი Set Theory & Logic

Relations, functions and equivalenceCardinality and infinityLogic and methods of proof