Let $2 = \{ 0, 1 \}$ and $X$, $Y$ be sets.
102777
Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$)
45216
Cardinality of $[0,1]$
123613
Double Complement of a set proof
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
150790
Prove two sets have same Cardinality by writing down bijection
9149
Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
23764
Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
153492
Let $p\colon X \to Y$ be a quotient map then if each set $p^{-1}({y})$ is connected, and if $Y$ is connected, then $X$ is connected.
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
59813
Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
46622
Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.
117658
A set with n elements has 2^n subsets