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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).

ምሳሌ · {1,2,3,4} union {3,4,5,6}

Set-Theory · Sets

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

እርምጃ በደረጃ

  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|.

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

አሁን ችግርን ይምረጡ፣ ወይም ጻፉ ወይም በራሳችሁ ቅርጽ አቅርቡ። እርምጃው ሁሉ፣ ምስል፣ መልሱ እስከምትጠይቅ ድረስ የተደበቀ ነው።

የራስዎን ስራዎች ይያዙ

ነጻ የሆኑት መተግበሪያዎች በየክፍል ውስጥ ማስታወሻዎችን ያካትታሉ፣ የተጠናቀቁትን ነገሮች መዝገብ፣ የተፈቱ ችግሮችን በአንድ ቦታ፣ ስለዚህ ገጽ መጠየቅ የሚችሉትን ረዳት ያካትታሉ፡፡ የቁጥር ትምህርት ለሁሉም ሰው ክፍት ነው፣ ተቀባይነት ያለው ወይም የለም፤

ምዝገባ መግባቱ

ፊደላት

ለሙሉ መግለጫ፣ ምስል፣ እና በውስጡ ያለውን ፊደል ትርጓሜ ለማየት ማንኛውንም ምልክት ይጫኑ።

እንዴት: 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|.

ጥያቄዎች

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.

በ Set Theory & Logic

Relations, functions and equivalenceCardinality and infinityLogic and methods of proof