Finding Power Set Examples | Set Theory, Subsets and Power Sets

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.

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.

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+WRATH OF MATH+


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[datboi]

Thanks so much for this video. The little tip with the combination formula really helped a ton with solving power sets.

[bryanherrera]

You made me understand this topic of power sets. Thank you so much!

[willardmakinishi]

Tanks Man this is really powerful and precise

[bashiribrahim]

How can u know on how to check the subsets example like the formula you use 4!/2!

[zaiba]

After lookin at this it's pretty easy thnks for this 😃✌️

[NomanKhan-imze]

Seeing this after 4 years😂thank u for reminding how to find power sets

[SamuelJulius-njjh]

Can you do for a set with six elements?

[zaiba]

And as u said can u make a video on derivatives?

[claudiamesaaparicio]

Hi. Can we see a videos about proof of problem NPTime or NP-hard?

[hello-gtsu]

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?

[parcell]

Ohh, so we did have a cruel teacher who gave us 5 elements in a set to write the powerset in just 1 minute.😅

[divyanshutiwari]

Sir make a complete python playlist it will be very helpful

[dhairyakumarsahu]

How did you got 6 please explain, I have my exam tomorrow

[paramapurni]

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?

[hunnybowbarasa]

What about power sets of more than three elements

[detective]

Please help me out on set proposition or set proof

[peacewhosiargao]

how about this Let A= {{1, 2}, 3, 4} determine |P(P(A))|??

[lesterdavepaguio]

can a subset be an element of the power set?

[kuyaharlan]

plss..help me solved this🙏Let z ={a, b}.find the power set of z.

[AshleyPhiri-yr]

Kindly find a power set of B={1{1, 3} }