Set Identities | Generalized Union and Intersection | Set Theory | Maths for CS | CS Connect 15

This video will explain set identities using Venn Diagrams. Along with that, the following topics will be discussed:
- Duality Principle
- Membership tables
- Generalized union and intersection
Practice problems are provided for:
- proving identities using subsets and membership table,
- generalized union and intersection with various sets

00:00 Intro
00:21 Laws of Algebra of Sets
01:00 Identity laws
02:28 Domination laws
03:32 Idempotent laws
03:59 Complementation law
04:47 Complement laws
06:02 Commutative laws
07:18 Associative laws
09:31 Distributive laws
12:01 De Morgan's laws
14:43 Absorption law
15:55 Summary of Set Identities
16:11 Principle of Duality
19:02 Membership tables
25:42 Generalized unions and intersections
28:38 Practice Problems
28:42 1. Show LHS = RHS by showing each side is a subset of the other side and by using membership table.
35:59 2. Find generalized union and intersection of set Ai (i = 1 to n)
39:23 3. Find generalized union and intersection of set Ai (i = i to infinity) for every positive integer i
39:29 a) Ai = {-i, -i+1, ..., -1, 0, 1, ..., i-1, i}
41:14 b) Ai = {-i,i}
42:52 Working with intervals of real numbers
44:32 c) Ai = [-i,i], the set of real numbers x
46:23 d) Ai = [i,infinity), the set of real numbers x

Set Theory Playlist:
https://www.youtube.com/playlist?list=PLQqPPVnzZIy5K5fWsoFAFWG5j8eHspZ--

Mathematics for Computer Science Playlist:
https://www.youtube.com/playlist?list=PLQqPPVnzZIy6qB_345OS7qzKyoJjj1urI

CS Connect Playlist:
https://www.youtube.com/playlist?list=PLQqPPVnzZIy5BmFckmCIEAysYf0zDwQiB

CS Connect File:
https://docs.google.com/presentation/d/e/2PACX-1vToDoGrjlp8KcxOtP1HT5wJ0ciZrIakYbfSL_jqzRN5-3DaRtDA6LsRYxz_a9Hct7CzgnHcE3CIalt2/pub

Видео Set Identities | Generalized Union and Intersection | Set Theory | Maths for CS | CS Connect 15 канала Computer Science Brainery