Let p$,$ q$,$ and r be the propositions: p: "The flag is set",q: $"$I$=0"$r: "Subroutine S is completed."Translate each of the following propositions into symbols, using the letters p$,$ q$,$ or r and logical connectives. a$)$ If the flag is set, then I$=0.$ b$)$ The flag is set and I$=0$ if subroutine S is not completed. c$)$ Subroutine S is completed if and only if I$=0$ and flag is set.