Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc) - Counting with Triple Intersections // Example & Formula

Suppose three sets overlap such that they have a triple intersection of all three sets. How many elements are there total? In this video we will explore a counting argument when we have a Venn Diagram which is a union of three sets, and will see how to use the data about how many there are in the double and triple intersections to compute the total number of elements. It's helpful to begin with the union of just two sets. The the formula is N(A union B) = N(A)+N(B)-N(A intersect B). The reason is that elements of the intersection of A and B are counted twice in N(A) and N(B) respectively, so in order to be counted only once need to be subtracting. Extending the idea of the union of three intersecting sets, the counting formula becomes : N(A U B U C)= N(A)+N(B)+N(C)-N(A intersect B)-N(A intersect C)-N(B intersect C)+N(A intersect B intersect C) This video is part of my course on Discrete Math. Full playlist below. **************************************************** COURSE PLAYLISTS: ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►DIFFERENTIAL EQUATIONS (Calc IV): https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 *************************************************** ► Want to learn math effectively? Check out my "Learning Math" Series: https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Want some cool math? Check out my "Cool Math" Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho **************************************************** ►Follow me on Twitter: http://twitter.com/treforbazett ***************************************************** This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria. BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett