Proof: If A is a Subset of B then C-B is a Subset of C-A | Set Theory

Показать описание

If A is a subset of B then C-B (the relative complement of B with respect to C) is a subset of C-A. We prove this basic set theory result in today's set theory lesson!

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.

********************************************************************

+WRATH OF MATH+

Follow Wrath of Math on...

Рекомендации по теме

Комментарии

OMG YOU ARE SO HELPFUL 😭😭😭😭😭 IM RECOMMENDING THIS TO MY WHOLE UNIVERSITY CLASSS (we have a horrible professor) PLEASE KEEP UP THE GOOD WORK

spacecommunityv.i.d.a

This was incredibly helpful, thank you!

xilinchoi

Sir you taught good but can show with examples it with proof so that we can try to understand more

chintankae

Let s be an element of C - B. This means s is an element of C but not B, and as A is a subset of B, s is not an element of A either, but still an element of C. Therefore s is an element of C, but not A meaning an element of C - A. In conclusion, C - B is a subset of C - A.

azizhani

• 0:49 - Huh? No, if A⊆B, then B might have stuff that A doesn't have, so if you remove B from C, then it's impossible for C to have elements of A left over since all of A was in B which were removed.
• 1:02 - Wait, what‽ 🤨 That's not a subtraction of B, it's a subtraction of just the intersection with B. C-B would imply that B is a subset of C and all of B is taken out. In other words, this isn't *C-B* it's *C-(C∩B).* 🤔 Hmm, it seems that set subtraction is poorly defined, it seems that _A-B = A-(A∩B)_ (which is pretty sloppy for such a strict discipline 😕).

vnceigz

Proof: If A is a Subset of B then C-B is a Subset of C-A | Set Theory

Set Theory Proof A is a subset of B if and only if A intersect B = A

Set Theory Proof: If A n B = empty! then A is a subset of B complement

Discrete Math - 1.8.1 Proof by Cases

Proof that if g o f is Surjective(Onto) then g is Surjective(Onto)

How to do a PROOF in SET THEORY - Discrete Mathematics

Proof: A is a Subset of B iff A intersect B Equals A | Set Theory, Subsets

Discrete Math - 1.7.1 Direct Proof

Discrete Math 1.8.1 Proof by Cases

Methods of Proof | A-level Mathematics

Proof: If There is a u-v Walk then there is a u-v Path | Every Walk Contains a Path, Graph Theory

Discrete Math - 1.7.2 Proof by Contraposition

Proof: A is a Subset of B iff A Union B Equals B | Set Theory, Subsets

Proof by Contrapositive | Method & First Example

Proof by Contradiction | Method & First Example

Discrete Math - 1.7.3 Proof by Contradiction

Proof: A is a Subset of B iff B' is Subset of A' | Set Theory, Subsets, Set Complement

[Proof] Function is bijective

Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)

Discrete Math 1.7.2 Proof by Contraposition

Direct Image of Union of Sets Proof: f(A U B) = f(A) U f(B)

The 360-Page Proof That 1+1=2

Set Theory Proof: A subset of B and C subset of D then A x C is a subset of B x D

Digital Electronics: Proof of a Boolean Identity (A+A'B=A+B)

Proof: Supremum and Infimum are Unique | Real Analysis