$(A\times B)\cap (C\times D)=(A\cap C)\times (B\cap D)$: Proof Strategy for Cross Products of Intersected Sets
59644
Proof of Cartesian product intersection
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
56440
Cartesian products and families
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
123613
Double Complement of a set proof
74311
Proving that the Intersection of any Collection of Compact Sets is Compact
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
38807
Does set difference distribute over set intersection?
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
61666
Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
130156
Image of the union and intersection of sets.
42883
Cross product in $\mathbb R^n$
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
74077
A intersection (A union B)