Number of Subsets Containing a Set of Elements | Set Theory, Combinatorics

How do we count the number of subsets that contain a particular collection of elements? We'll be answering this question with an example and a general solution in today's video set theory lesson!

SOLUTION TO PRACTICE PROBLEM:

There are 4 elements of S, so S has 2^4 subsets total. How many subsets contain y and z? Well, to make such a subset we have one choice for y and z (to include each of them) and 2 choices for w and x, so the total number of subsets of S containing y and z is 2^(4-2) = 2^2 = 2*2 = 4. Let's list them: {y, z}, {y, z, x}, {y, z, w}, {y, z, w, x}.

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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[damadorian]

I’m a matah teacher form Turkey and i really liked the way you approach to it

[manikyagandhigunasekar]

This gave me the answer to all my problems in life right now, thank you!

[zacksnyder]

Can I please ask you a specific question? how many subsets of {1, 2, 3, …, 20} are there with no more than 2 consecutive integers? Please also explain fully how you arrived at the answer.

[andrewjustin]

5:50 Would you please elucidate your point why it adds up when we say x=A, which means 2^(n-|x|) becomes 2^(n-n) or 2^(0) or 1 that means there is only one element of A that contains all element of A, which is A itself.

[cynthiagenvieve]

how do you find the number of elements of a set that has a given number of subsets?

for example something like 64 subsets

[robloxumegalux]

What if the question given to you is how many subset are therein a set containing two elements