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Explain AUB = Union of set A and set B = {x : x ε A or x ε B (or both)}.what is the...

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rishabh050996 | Student, Grade 10 | eNoter

Posted April 6, 2010 at 2:57 AM via web

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Explain AUB = Union of set A and set B
= {x : x ε A or x ε B (or both)}.what is the meaning of x

and ε here?

Tagged with math, set theory

3 Answers | Add Yours

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justaminotaurtoo | Teacher | eNotes Newbie

Posted April 6, 2010 at 3:24 AM (Answer #1)

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x is a variable.  ε is a symbol which means 'belongs to' so if x ε A then x is an item in the set A.

Example.  If the value of x is 'Chihuahua' and A is the set of all dogs then you could say x ε A.  If the value of another variable, y, is 'Gun' and B is the set of all dangers then you can say y ε B.

These are just mathematical ways of saying Chihuahuas are dogs, and guns are dangerous.

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neela | High School Teacher | Valedictorian

Posted April 6, 2010 at 3:33 AM (Answer #2)

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AUB implies the following:

x could blong to A only or

xcould belong  to A and x could belong to B  both.

x could belong to B only.

The above three subsets  are mutually exclusive or which can materialise  one at a time.

 

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giorgiana1976 | College Teacher | Valedictorian

Posted April 7, 2010 at 1:21 AM (Answer #3)

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A set is a well-defined collection of objects and it is considered as a whole. Objects from a set are called elements. Elements of a set can be of any kind: numbers, persons, letters of the alphabet, other sets, etc. Sets are denoted by italic capital letters A, B,etc.

The concept that describes whether or not an element is part of a certain set (ie, whether it belongs to the set) is denoted by the symbol . 

So, x ε A or x ε B, means that the element x is belonging to the set A or the set B.

Two sets can be "added" and the operation of addition is called "union" of A and B and it is noted AUB, where the result is the set of all entities that are members of either  A or B.

x represents each of all entities resulted from the union of A and B.

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