Does ℘(A ∩ B)=℘(A) ∩ ℘(B) hold? How to prove it?
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
10107
Prove $A\cup (A\cap B) = A$
67717
$A \oplus B = A \oplus C$ imply $B = C$?
142026
Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
86030
Prove or disprove - If a divides b and b divides a does a=b
59813
Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
110381
Prove that if rank(A + B) = rank(A) + rank(B), then col(A) ∩ col(B) = {0}
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?