Finding the Number of Subsets of a Set (Example Problems)
209.9 هزار بار بازدید -
5 سال پیش
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How do we find the
How do we find the number of subsets a set has? How many subsets does any given set has? In this video we go over some example problems, calculating the number of subsets a set has.
To do this, we have to figure out how many elements our set has. Say it has n elements. Then, it has 2^n subsets! It's a simple formula with a simple explanation we address in the video, and I go over it in more detail in this lesson: Formula for Cardinality of Power Sets...
In the examples in this video, we look at sets written in roster method. Sometimes, it can be tricky to identify elements in sets written like this. Here is a video on identifying the elements of a set written in roster method: How to Identify the Elements of a Set...
SOLUTIONS TO PRACTICE PROBLEMS:
1. The empty set has 0 elements, so it has 2^0 = 1 subsets. The only subset of the empty set is the empty set itself.
2. This set has 6 elements. They are the numbers 3, 4, and 7, the set { 3, 4, 7 }, and the numbers 34 and 73. Thus, it has 2^6 = 64 subsets.
3. This set has 8 elements. They are the numbers 4, 2^3, 0, and 2, the interval [1, 2], the sets { 1, 9, 10 } and { }, and the 3-tuple (2, 3, 4). Thus, it has 2^8 = 256 elements.
How did you do?
◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Abstract Algebra: https://amzn.to/3IjoZaO
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd
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: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtu...
Vallow SoundCloud: SoundCloud: benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: Patreon: wrathofmathlessons
Follow Wrath of Math on...
● Instagram: Instagram: wrathofmathedu
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● Twitter: Twitter: wrathofmathedu
My Music Channel: seanemusic
To do this, we have to figure out how many elements our set has. Say it has n elements. Then, it has 2^n subsets! It's a simple formula with a simple explanation we address in the video, and I go over it in more detail in this lesson: Formula for Cardinality of Power Sets...
In the examples in this video, we look at sets written in roster method. Sometimes, it can be tricky to identify elements in sets written like this. Here is a video on identifying the elements of a set written in roster method: How to Identify the Elements of a Set...
SOLUTIONS TO PRACTICE PROBLEMS:
1. The empty set has 0 elements, so it has 2^0 = 1 subsets. The only subset of the empty set is the empty set itself.
2. This set has 6 elements. They are the numbers 3, 4, and 7, the set { 3, 4, 7 }, and the numbers 34 and 73. Thus, it has 2^6 = 64 subsets.
3. This set has 8 elements. They are the numbers 4, 2^3, 0, and 2, the interval [1, 2], the sets { 1, 9, 10 } and { }, and the 3-tuple (2, 3, 4). Thus, it has 2^8 = 256 elements.
How did you do?
◉Textbooks I Like◉
Graph Theory: https://amzn.to/3JHQtZj
Real Analysis: https://amzn.to/3CMdgjI
Proofs and Set Theory: https://amzn.to/367VBXP (available for free online)
Statistics: https://amzn.to/3tsaEER
Abstract Algebra: https://amzn.to/3IjoZaO
Discrete Math: https://amzn.to/3qfhoUn
Number Theory: https://amzn.to/3JqpOQd
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
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: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtu...
Vallow SoundCloud: SoundCloud: benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: Patreon: wrathofmathlessons
Follow Wrath of Math on...
● Instagram: Instagram: wrathofmathedu
● Facebook: Facebook: WrathofMath
● Twitter: Twitter: wrathofmathedu
My Music Channel: seanemusic
5 سال پیش
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