How do you even prove a set theory subset statement using element argument? I simply just can't find any relevance to the question with the notes i was studying.
Any guidance would be much appreciated.
(A – B) ∩ (C – B) subset of (A ∩ C) – B
The only definition i have is
x element of A – B is logically equivalent to ( x element of A and x
not element of B)
If i were to sub in the definition, it would lead me to nowhere where i can use whatever law there is in set theory.
This discrete mathematics is way different from the typical maths i have been doing since young. Any guidance is appreciated.
Best Answer
Note that $$x\in(A-B)\cap (C-B) $$ is equivalent to $$x\in A-B\quad \land \quad x\in C-B $$ and so to $$(x\in A \land x\notin B)\land (x\in C\land x\notin B). $$ Form this you want to show that $x\in(A\cap C)-B$, or equivalently, that $$(x\in A\land x\in C)\land x\notin B. $$ I guess you can take it from here.