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?

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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.

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.

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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