Задача 2.

Show that for any $a$, $b$, $c$, $x$, $y$ the following is true: 1) if $b \mid a$ and $c\mid b$, then $c\mid a$; 2) if $a⋮ b$ and $a\ne0$, then $|a|\geqslant|b|$; 3) if $c\ne0$, then $a⋮ b\Longleftrightarrow ac⋮ bc$; 4) if $a⋮ b$ and $c⋮ b$, then $(a\pm c)⋮ b$; 5) if $a⋮ b$ and $c⋮ b$, then $ax+cy ⋮ b$; 6) if $a⋮ b$ and $b⋮ a$, then $a=b$ или $a=-b$; 7) if $a⋮ b$, then $ac⋮ b$; 8) if $a⋮ b$ and $b \nmid c$, then $b \nmid (a+c)$; 9) if $ab=cd$ and $a⋮ c$, then $d⋮ b$.