Finding Power Set Examples | Set Theory, Subsets and Power Sets
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- čas přidán 24. 07. 2024
- How do we find the power set of a set? That's what we'll go over in today's set theory video lesson with 4 examples!
Remember the power set of a set S is the set P(S) consisting of all subsets of S. Don't forget to include the empty set and the set S itself! Also recall that the cardinality of the power set of S is equal to 2 to the power of the cardinality of S.
Lesson on power sets: • What is a Power Set? |...
Why the Empty Set is a Subset of Every Set: • Why is the Empty Set a...
Lesson on the power set of the empty set: • What is the Power Set ...
Formula for Cardinality of Power Sets (2^n): • Formula for Cardinalit...
What is the cardinality of a set?: • What is the Cardinalit...
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: vallow.bandcamp.com/
Vallow Spotify: open.spotify.com/artist/0fRtu...
Vallow SoundCloud: / benwatts-3
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+WRATH OF MATH+
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You made me understand this topic of power sets. Thank you so much!
Thanks so much for this video. The little tip with the combination formula really helped a ton with solving power sets.
My pleasure, glad it helped and thanks for watching!
Tanks Man this is really powerful and precise
Hi. Can we see a videos about proof of problem NPTime or NP-hard?
Great video
This is really helpful! Thank you
You're very welcome! Thanks for watching!
Can you do for a set with six elements?
Thank you 😊 you helps me a lot
Glad it helped! You're welcome and thanks for watching!
This is great!!!!
Thank you, Noah! Let me know if you ever have any questions!
Thank you so much bro🙂 Long live!
You’re very welcome! I am glad it helped and thanks for watching!
can u explain binary relation
Well done.. thanks a lot..
My pleasure, thanks for watching!
How can u know on how to check the subsets example like the formula you use 4!/2!
I ‘ll tell you how to check the subset ...
Look at this example -
Ex-1 :
For example your formula is -
C = { 2,3,6}
And then if the question comes like -
“ Is 2 a subset of this set “ ?
Then your answer will be “ 𝘆𝗲𝘀 “,
2 is a subset of this whole set because 2 is an element of this set . If you want to know it briefly, you can say that this set has the number “2” , this is why two is a subset of this set ( Set C ) ...
In mathematical formula, you write this way -👇👇👇
2 ⊆ C
Meaning ( 2 is a 𝘀𝘂𝗯𝘀𝗲𝘁 of Set C )
* We write “ Set C” because this set is denoted using the letter “ C” ...
You can also use another method to write in mathematical way , and that is...
👇👇
2 ⊆ { 2, 3,6 }
Meaning- 2 is a subset of set 1,2,3 ..
⊆ - 👈 ( this is the symbol of subset )
And ...
If there is any question like ...
“ Is 7 are subset of * Set C * ? “
Then you’re answer would be “ 𝗻𝗼“ ..
Guess why , ? Because 7 is 𝗻𝗼𝘁 an element of this set ..
( I am talking about the same set that I gave before ) !!
And briefly you can say the number 7 is 𝗻𝗼𝘁 in this set !
So in mathematical way , you’ll write ...
7 ⊄ C
Meaning : 7 is not a subset of Set C
You can also write in this way as :
7 ⊄ { 2,3,6 }
Meaning - 7 is 𝗻𝗼𝘁 𝗮 𝘀𝘂𝗯𝘀𝗲𝘁 of set 2,3,6
If you have any other Question , please let me know , don’t worry , i’ll help you ! 😇😇
Im still din understand the factorial numbrr how he get 6 here from 4 / 2! (4-2)!...can u help to explain how to derive this factorial calculation..
Thank you very much 😊❤️😊❤️😘
My pleasure, thanks for watching!
how about this Let A= {{1,2},3,4} determine |P(P(A))|??
Thanks this was helpful
Glad to hear it, thanks for watching!
Nice explanation
Thank you!
After lookin at this it's pretty easy thnks for this 😃✌️
My pleasure, glad it helped!
May God blesses you.😊
Thank you so much .
My pleasure! Thanks for watching and let me know if you ever have any video requests!
Wrath of Math
🤍💎 yes please 💎🤍
1- permutations
2- r-permutations
What about power sets of more than three elements
Seeing this after 4 years😂thank u for reminding how to find power sets
Your comment freaked me out, this video was uploaded 9 months ago, not 4 years ago 😂 Making me feel old! Glad it helped though!
@@WrathofMath 😂😂 i meant power sets 😂🤦🏻♂️am seeing em after 4 years
@@WrathofMath it really helped thank u
Please help me out on set proposition or set proof
Thanks for watching, Gideon! I'm not sure what you're asking, do you have a particular proof in mind? I have tons of examples of set theory proofs on my channel, just search for whatever you're looking for. Like "subset proofs wrath of math" or "set equality proofs wrath of math" will both bring up all sorts of videos.
you said "if the empty set wasn't a subset of the empty set that would mean that the empty set contains an element that the empty set doesn't and obviously that's not true because the empty set has no element." what did you mean by that ?? i don't understand that.
Second. i see that an empty set has no element so if we calculate the number of subsets of the power set 2^0 = 1 so the power set has only 1 element but i don't understand why. how do we prove that?
And as u said can u make a video on derivatives?
Thanks for watching and more calculus lessons are coming! Currently my focus for lessons is the Real Analysis playlist, but I will also be working on other stuff! Also, there is this recent video I did on a particular derivative: czcams.com/video/iS27bcO2Qm8/video.html
Can you help me solving this one please
You roll a four-sided (1, 2, 3 and 4) die 3 times. For this problem we’ll use the sample space with 64 equally likely outcomes.
a. Write down this sample space in set notation.
b. List all the outcomes in each of the following events.
(i) A = ‘Exactly 2 of the 3 rolls are fours’
(ii) B = ‘At least 2 of the 3 rolls are fours’
(iii) C = ’Exactly 1 of the second and third rolls is a 4’
(iv) A∩C
c. Find the probability for sets in question b. that is, P(A), P(B), P(C) and P(A ∩ C)
d. Are A and B independent events?
Did you find the answer , if you did can you post it please 🙏
can a subset be an element of the power set?
Thanks for watching and I am not sure what you're asking. By definition, the power set of A contains all subsets of A, so certainly by definition all elements of a power set are subsets of some other set.
Perhaps you're asking if a set can be an element of its own power set. Since every set is a subset of itself, by definition every set is an element of its own power set. Does that answer your question?
Wrath of Math yes it does. Thank you very much!!! I was just confused about subsets and elements in the power set. Thank you again!!! 🙂🙂
0:44 "what the heck is that" love it.
Haha, thanks for watching! Let me know if you ever have any questions!
Thank's bro
My pleasure, thanks for watching and let me know if you ever have any questions!
@@WrathofMath nice to know there are still good people left in the community
plss..help me solved this🙏Let z ={a,b}.find the power set of z.
Powerset is the set of all subsets of a given set, and for every element there are exactly two possibilities: either it is an element of the subset, or it is not.
give a lecture on algebra plz
What sort of algebra do you mean?
How did you got 6 please explain , I have my exam tomorrow
Thanks for watching and I'm not sure what you mean, there were only 5 examples in the video. Could you clarify your question?
@@WrathofMath , Thanks for answering , I was asking about the factorial part , I got that clear by my brother .
Thank you , Love from INDIA
Glad your brother could help, let me know if you ever have any other questions! Much love back from the USA!
I’ve made my 100th like here...
Thank you!
thanks bro tomorrow is my exam
Ohh, so we did have a cruel teacher who gave us 5 elements in a set to write the powerset in just 1 minute.😅
plz post avideo of venn diagram
Kindly find a power set of B={1{1,3} }
Not {1{1,3} but {1{2,3} }
i didnt get nothing.
Sorry it wasn't clear. Do you have any questions I can help clear up?
@@WrathofMath at 2:46 i understood the 2 because its 2 choices per element but at 1:41 u wrote 2 to the power of its cardinality which is 0, but in 2:45 u wrote 2 to the power of its cardinality which you used |S|, why is that?...sorry for my english!
At 1:41 I could have written 2^|S|, but that's the same as 2^0 since, in that example, |S| = 0. At 2:45, S is a different set, we are in a different example. Then I wrote 2^|S|, just to remind you of the general formula being used, and in this case |S| = 1, so 2^|S| = 2^1. Does that help?
@@WrathofMath omg thank u so much man!! i was literally confused the whole day!!
Yahe video Urdu m banae
nooooo
YESSSSS! Do you have any questions I can help answer?
@@WrathofMath i want to learn this
my teacher made me write the power set with four elements :( 9:42
Can you do for a set with six elements?