$(1)$ Show that the following argument is invalid:

$plongrightarrow{r}^{{?}^{?}}q$

$not{q}^{{?}^{?}}$nots

notplongrightarrowsvvt

:$.t$

$(2)$ Prove using direct method that if $x$ and $y$ are integers and $x+y$ is odd, then $x-y$ is odd.

Assume

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$(3)$ Prove by contradiction that for any integer $n,n^2+2$ is not divisible by $4.$

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