$f[A\cup{B}]=f[A]\cup{f[B]}$
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
102917
Proving statement - $(A \setminus B) \cup (A \setminus C) = B\Leftrightarrow A=B , C\cap B=\varnothing$
86105
Can $\{(f(t),g(t)) \mid t\in [a,b]\}$ cover the entire square $[0,1] \times [0,1]$ ?
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
52787
If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
107383
Derived sets - prove $(A \cup B)' = A' \cup B'$
27899
Can we prove the existence of $A\cup B$ without the union axiom?
151852
How to prove $A \subset B \iff A \cup B = B$
118154
$f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ twice
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
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 $.
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