Proof: Subset is a Transitive Relation | Set Theory, Subsets, Transitivity скачать в хорошем качестве

Proof: Subset is a Transitive Relation | Set Theory, Subsets, Transitivity

We use the subset relation a lot in set theory, and it's nice to know that this relation is transitive! So if A is a subset of B and B is a subset of C, the transitive property of subsets tells us that A is also a subset of C. This should seem reasonable, if C contains B and B contains A, of course C also contains A. In today's video set theory lesson, we will prove this property for subsets just to be sure! The proof is very straightforward. If A is the empty set, it is certainly a subset of C. If A is not the empty set, let a be any element of A. Then a is an element of B since A is a subset of B. Thus, a is a element of C since B is a subset of C. Therefore every element of A is an element of C and hence A is a subset of C. Lesson on why the empty set is a subset of every set:    • Why is the Empty Set a Subset of Every Set...   If you are preparing for Set Theory or in the midst of learning Set Theory, you might be interested in the book I learned set theory and proofs from. It is “Book of Proof“ by Richard Hammack. Check out the book and see if it suits your needs! You can purchase the textbook using the affiliate link below which costs you nothing extra and helps support Wrath of Math! PURCHASE THE BOOK: https://amzn.to/2TwTzG0 Or download the book for free: https://www.people.vcu.edu/~rhammack/... 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:   / benwatts-3   ******************************************************************** +WRATH OF MATH+ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Facebook:   / wrathofmath   ● Twitter:   / wrathofmathedu   My Music Channel:    / seanemusic