Proof: Cartesian Product with Set Intersection | Set Theory

We prove that the cartesian product distributes over set intersection. That is, we'll prove that Ax(B intersect C) = (AxB) intersect (AxC). To prove this set theory result, we'll use what's sometimes called double inclusion. This means we'll prove Ax(B intersect C) is a subset of (AxB) intersect (AxC) and (AxB) intersect (AxC) is a subset of Ax(B intersect C). This establishes the equality of the two sets. #SetTheory

For this proof, you should be comfortable with the definition of subset, intersection, and cartesian products. We'll repeatedly apply the definitions of these terms to complete the set equality proof.

What is a Subset?    • What is a Subset?  
Set Intersection:    • What is an Intersection? (Set Theory)  
What is the Cartesian Product of Two Sets?    • What is the Cartesian Product of Sets...  

★DONATE★
◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons  
◆ Donate on PayPal: https://www.paypal.me/wrathofmath

Thanks to Robert Rennie, Barbara Sharrock, and Rolf Waefler for their generous support on Patreon!

Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/

Follow Wrath of Math on...
● Instagram:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu  

My Music Channel:    / @emery3050