The notation $\{f(x)$:xinS$\}$ means "the set of all values that can be produced by substituting an element $x$ of set $S$ into $f(x)."$ For example, the set of all odd integers can be expressed as $\{2k+1$:kinZ$\}.$

Let A and $B$ be sets defined as follows:

$A=\{15m+2$:minZ$\}$

$B=\{3n-7$:ninZ$\}$

$($a$)(1$ point$)$ List any three elements of $A.$

$($b$)(1$ point$)$ List any three elements of $B.$

$($c$)(3$ points$)$ Prove algebraically that AsubeB. Hint: Use the definition of subset. AsubeB if every element of $A$ is also an element of $B.$