Show that it is impossible that $P(a)=b$, $P(b)=c$, and $P(c)=a$ at the same time.
1962
Polynomial $P(a)=b,P(b)=c,P(c)=a$
33633
Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
150282
If $A$ is independent of $B$ and $C$ then why is it not necessarally independent of $B\cap C$?
95800
Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$.
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
22584
Can we prove that a statement cannot be proved?
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
86893
Show that it is impossible to list the rational numbers in increasing order
35370
Why is this proposition provable and its converse not?
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$