How to prove A ⊆ B ⇒ C \ B ⊆ C \ A
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
142026
Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
77286
Proving set theory question
134120
Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
107173
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$
70552
Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
67717
$A \oplus B = A \oplus C$ imply $B = C$?
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
109778
Proving $(x-c)|(p(x)-p(c))$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
43068
Let A and B be sets. Show that A is a subset of B if and only if for any set C, one has A union C is a subset of B union C.