Proof for If $f : A \rightarrow B$ and $C \subseteq A$, then $f^{-1}(f(C)) \subseteq C$.
108633
Why $f^{-1}(f(A)) \not= A$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
83714
$A \in B$ vs. $A \subset B$ for proofs
154001
$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
121993
Prove that $f$ is one-to-one iff $f \circ h = f \circ k$ implies $h = k$.
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
104757
If $f \circ g$ is surjective, then f is surjective
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
65923
How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant