Preimage of Intersection of Two Sets = Intersection of Preimage of Each Set : $f^{-1}(A \cap B) = f^{-1}(A) \cap f^{-1}(B)$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
10477
Finding the closure of A=$\mathbb Q \cap [0,1]$.
141806
Prove that a nest of sets has an empty intersection
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
124467
Can $(X_1,X_2) \cap (X_3,X_4)$ be generated with two elements from $k[X_1,X_2,X_3,X_4]$?
18913
How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
74796
Extension of intersection of ideals
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
41347
The dimension of the intersection of two vector subspaces
23521
Power Set of $X$ is a Ring with Symmetric Difference, and Intersection
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
70538
Intersection and union of simply connected domain
133611
Intersection of two vector spaces