Subsets and Proper Subsets

Mahalo math expert Allison Moffett teaches viewers about subsets and proper subsets.

Sample Set
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Set A contains the elements a, b and c.

Subsets
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A subset is either all of the elements of a set or just some of the elements. This is its mathematical symbol: ⊆.Because b and c are elements of set A, {b,c} ⊆ A.Because a, b and c are in set A, {a,b,c} ⊆ A.

Example
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B = {1,2,6,8}{1,8,6} ⊆ B{8,6,2,1} ⊆ B

Proper Subsets
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A proper subset is a subset that contains some, but not all, of the elements of the original set. This is its mathematical symbol: ⊂.{b,c} is a proper subset of set A, because one of set A's elements is missing. {b,c} ⊂ A. {a,b,c} is not a proper subset of set A, because it contains all of set A's elements.

Example
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B = {1,2,6,8}{1,8,6} ⊂ B{8,6,2,1} is not a proper subset.

Empty Sets
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If a set has no elements in it, it is an empty, or null, set, shown as ∅. This is an empty set: { }.Because an empty set contains no elements, it is a subset of all sets.The logic behind this is that because there are not any elements in the empty set that are not in any given set, it must be true that all elements in the empty set are in any given set.Because an empty set does not contain the elements of any set but itself, it is a proper subset of every set but itself.c

Example
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B = {1,2,6,8}B ≠ {3,4}{ } ≠ {3,4}{ } ⊆ B{ } ⊂ B{ } is not a proper subset of { }.

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[erickalewis]

In just 1 min you gave me a more clear understanding than I got in about 5 hours. Thanks.

[Cyranek]

couldnt focus cause im thinking about how insane it is that she has to write everything mirrored

[sky]

im in college, but this video made me feel like i was in pre-school again when everything was so easy and clear.. thanks

[mahalodotcom]

@BeeS0Chic Why, do you like it? We have stock samples for our videos here at Mahalo, and that was a little beat I mixed myself during some downtime at work. Thanks for the awesome feedback!

You just made my day :)

[JuniorRomero]

why did you write bc and bc and you said they are not both proper subsets???

[edlopez]

I'm a bit confused. You mention that {b, c} is a subset of A, then you said that {b, c} is a proper subset of A. Can you explain that? How can it be both a subset and a proper subset? Thanks.

[stegi]

You just saved my mathematics for computing module, my proffesor waffles too much!

[TaeTae-smzr]

This was our lesson during this module time uhuh

[sehlaramos]

that you so much I really needed help when learning it yourself is kinda harder

[LynGoh]

what's she writing on? and how is she able to write backwards?:O

[anwarsaeed]

What is the formula which is to find the numbers of topology on a given set? If i find it

[vimalkumarsharma]

Which software you have used to create video ?

[josephchloupek]

quick revise before a test thanks ! worked for me

[jeevankumarg]

can u solve the problem if a=(1, 2, 3)

[moa]

i like the idea of the mirror, nice job and thank you for the video.

[graceperez]

Do how to list proper subsets and subsets

[sayanttcfybsc]

you should tell about what is the answer of a subset

[shazianaeem]

What if A=1, 2, 3, 4, 5 and B=1, 2, 3.Then B is a proper subset of A or not

[MyPookie]

is the empty set a proper subset of every set ?

[saurabhrb]

How are you able to write on the glass in an inverted manner??