# Indirect proof problems with answers

Recent questions in Indirect Proof
Cheyanne Jefferson 2022-08-16

### Can we prove $\mathrm{¬}R\left(x\right)\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\mathrm{¬}R\left(y\right)$ by proving $\mathrm{¬}\mathrm{¬}R\left(y\right)\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\mathrm{¬}\mathrm{¬}R\left(x\right)$?Can we also prove that by proving $R\left(y\right)\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}R\left(x\right)$?

assuolareuz 2022-08-14

### Give a direct proof that the set $\left\{x|{\mathrm{\Phi }}_{x}\left(1\right)↓\right\}$ (which is a set of program numbers that halt on input $1$) is not recursive.

Ebone6v 2022-08-13

### Suppose $R$ is a partial order on a set $A$, and $B\subseteq A$.Prove that, if $R$ is a total order and $b$ is a minimal element of $B$, then $b$ is the smallest element of $B$.

pigskiniv 2022-08-12

### In an indirect proof, is it possible to reject the assumption based on contradiction of a premise?

yongenelowk 2022-08-11

### Proves directly that $lim sup\left\{{a}_{n}+{b}_{n}\right\}\le lim sup\left\{{a}_{n}\right\}+lim sup\left\{{b}_{n}\right\}$

Matonya 2022-08-11

### Show that $T\left(X\right)=\left(R,V\right)=\left({X}_{\left(n\right)}-{X}_{\left(1\right)},\frac{{X}_{\left(n\right)}+{X}_{\left(1\right)}}{2}\right)$is a minimal sufficient statistic for $\theta$.

Rose Graves 2022-08-10

### Is it possible to derive Peirce's Law:$⊢\ast \left[\left(\alpha \to \beta \right)\to \alpha \right]\to \alpha$in a calculus that has modus ponens, the Deduction Theorem, Cut rule, Inconsistency effect and Principle of Indirect Proof?

Leia Hood 2022-08-09

### Proof $5\mid n\phantom{\rule{thickmathspace}{0ex}}⟺\phantom{\rule{thickmathspace}{0ex}}5\mid {n}^{2}$

Jaylyn Gibson 2022-08-06