Subsets $A$ of $\Bbb{Z}$ such that $xy \in A \implies x \in A, $ or $y \in A$. Primality of arb. subsets.
67203
Complement of maximal multiplicative set is a prime ideal
147013
Subset of a finite set is finite
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
83714
$A \in B$ vs. $A \subset B$ for proofs
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
104855
Prove that $N \subset Z(G)$
134770
For sets $A,B$, $A \cap (B \setminus A) \subseteq \varnothing$
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
5118
Show that $n ≤ 100$ if $ \{A_1,A_2,... ,A_n\}$ is a set of distinct $3$-element subsets of $\{1, 2,... , 36\}$ such that...
117590
Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
17510
Proving a set is an abelian group.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime