$$Definition $3\mathrm{.}2$ Let p$,$ q$,$ and r be integers. A $3-$strand pretzel link Pp$,$q$,$r can be constructed as follows. Take three pairs of string segments and arrange them vertically. Twist the bottom ends of the first pair p times $($in the counterclockwise direction if p $>0$ and in the clockwise direction if p $<0).$ Twist the bottom ends of the second pair q times and the bottom end of the third pair r times.$$

Exercise $3\mathrm{.}2.$ For which values of p$,$ q$,$ and r is the link Pp$,$q$,$r a knot? For which p$,$ q$,$ and r does Pp$,$q$,$r have more than one component? Conjecture conditions on p$,$ q$,$ and r that determine the number of components in Pp$,$q$,$r and then prove your conjecture.

Please explain with context and drawing if you can. Thank you