If $A,B,C$ are sets and $|A \cup B| = |C \times C|$, prove that there is either a surjection from $A$ to $C$, or an injection from $C$ to $B$
58186
Set theory proof, $\exists g(g\colon A\twoheadrightarrow C)$ or $\exists h(h\colon C\hookrightarrow B)$
45792
Rigorous proof that surjectivity implies injectivity for finite sets
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
16092
How to prove that the composition of two surjective functions is surjective
76823
Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
150738
Proof of $(A - B) - C = A - (B \cup C)$
113211
Arithmetics of cardinalities: if $|A|=|C|$ and $|B|=|D|$ then $|A\times B|=|D\times C|$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
21663
Bijection between power sets of sets implies bijection between sets?
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
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.
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
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
57269
A special bijection between $\mathbb{R}\times \mathbb{R}$ and $\mathbb{R}$