How to prove $f(A\cap B)=f(A)\cap f(B) \quad \text{for every} \quad A,B⊂X$ when $f: X\rightarrow Y$ is injective?
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
6825
If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
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
152438
Is the composition of two injective functions injective?
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
10253
Proving that all entire & injective functions take the form $f = ax + b$?
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) $
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
97184
Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
23464
How to find a explicit bijection for some $f:A\times B \rightarrow B \times A$