Prove the set-theoretic identity for sets A and B: {2,2,2}={2}
97890
$\{1,1\}=\{1\}$, origin of this convention
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
151852
How to prove $A \subset B \iff A \cup B = B$
156566
Combinatorial proof of a binomial identity: $\sum_k \binom {2r} {2k-1}\binom{k-1}{s-1} = 2^{2r-2s+1}\binom{2r-s}{s-1}$
113083
How to prove a set equality?
72256
Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$
113290
Prove combinatorics identity
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
13906
How to prove the set $S$ is closed under the binary operation $a*b=a+b+kab$?
83714
$A \in B$ vs. $A \subset B$ for proofs
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
61747
Proof of exchange principle in set theory
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.