$(5$ points$)$ Consider the following four statements:

My program has a compile$-$time bug or a run$-$time bug or a logic bug.

My program compiles successfully if and only if my program does not have a

compile$-$time bug.

My program has a run$-$time bug if and only if my program crashes.

My program compiles successfully and it did not crash.

a$.$ Create sentential variables that correspond to the atomic propositions in the above

statements.

b$.$ Translate these four statements into four logical expressions.

What can you conclude from these four statements if they are all true? Explain.