Prove a set is a subset of another.
48797
Proving Two Sets are Equal - Infinite Sets - Example
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
59813
Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
83714
$A \in B$ vs. $A \subset B$ for proofs
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
77902
If $A,B,$ and $C$ are sets, then $A\times(B-C)$ = $(A \times B)$ $-$ $(A \times C)$.
132605
Finding the number of subsets of a set such that an element divides the succeeding element.
136755
Direct proof of empty set being subset of every set
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
9149
Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
41080
If A, B, and C are set and $A \subset B ,B \subset C \rightarrow A \subset C$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
2287
If a set is linearly independent, a finite subset of that set is also linearly independent
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
77286
Proving set theory question
7416
Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.