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Null SET {Ø} = Empty Set

by ez2
(Philippines)











































IS THIS TRUE OR FALSE AND WHY? : {Ø}⊂{} AND WHAT IS THE SUBSET OF {Ø}?

Comments for Null SET {Ø} = Empty Set

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Jun 24, 2012
Subset of Empty Set
by: STaff

The answer to your Math Question from our Online Tutor:



A Null Set Ø is a set which contains nothing (no elements).

For example:

Set Q is inhabited, and contains the following three elements:
x, y, z

Q = {x, y, z}

Set Ø (Null Set) is empty. It contains no elements: "nothing".

Ø = {}


The symbols Ø and {} mean exactly the same thing.

Because a Null Set contains no elements, it is also called an Empty Set. The two terms are synonyms for one another.

Ø (Null Set) is not the same as the number 0 (zero). The number 0 (zero) is a whole number.


⊂ is the symbol for a "PROPER (1) Subset (left) to Set (right)"


Q ⊂V means Set "Q" is a PROPER Subset of Set "V":

For Q to be a PROPER Subset of V: (1) Every element (without exception) contained in Set "Q" must also be present in Set "V".

+++ IMPORTANT >> And . . . (2) Set "Q" cannot be equal to Set "V". (Set "Q" must have a smaller number of elements than Set "V")

The math symbol ⊂ is equivalent to and is interchangeable with ⊊ (the equal sign at the bottom edge of the symbol is crossed out, indicating the subset cannot be equal to the set). Both symbols mean exactly the same thing: a "Proper" Subset.

In contrast, the subset math symbol ⊆ represents a subset, but not necessarily a Proper Subset.

Item (2), above, does not apply. If this symbol is used, it indicates that the subset (labeled "Q" in the example shown above) and the set (labeled "V" in the example shown above) CAN be equal.


>>> the final answer to your question is:

FALSE:

Ø⊂{} is false. Ø IS NOT a PROPER subset of {} since both sets contain exactly the same number of elements.


However, the following statement is TRUE:

Ø⊆{}




Thanks for writing.

Staff
www.solving-math-problems.com


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