Interpreting if-then statements

[Mr Davis 97]

Homework Statement

Rewrite the following as an if-then statement: Regular work is not necessary to pass the course.

Homework Equations

The Attempt at a Solution

Supposing that the "not" is not there, we would have "Regular work is necessary to pass the course." This means that "if the course was passed, then regular work was done." Now, if we include the not we get "it is not the case that if the course was passed, then regular work as done." Is this correct?

 

[LCKurtz]

Homework Statement

Rewrite the following as an if-then statement: Regular work is not necessary to pass the course.

Homework Equations

The Attempt at a Solution

Supposing that the "not" is not there, we would have "Regular work is necessary to pass the course." This means that "if the course was passed, then regular work was done." Now, if we include the not we get "it is not the case that if the course was passed, then regular work as done." Is this correct?

That doesn't strike me as an "if - then" statement. How about something like "If the course was passed, regular work may or may not have been done".

 

[Mr Davis 97]

That doesn't strike me as an "if - then" statement. How about something like "If the course was passed, regular work may or may not have been done".

In general how would you write "not necessary" as a conditional? I know that if we say "A is necessary for B" then B implies A. But I'm not sure how to write "A is not necessary for B" logically.

 

[LCKurtz]

I would say B does not imply A. But that might not be what you want. I will let others chime in here.

 

[Mr Davis 97]

I would say B does not imply A. But that might not be what you want. I will let others chime in here.

But the thing is is that it says to write as a conditional, and "B does not imply A" is not an if-then statement...

 

[member 587159]

I wonder who made these exercises.

 

[fresh_42]

Is necessary is the relation $\rightarrow$, so is not necessary means $\nrightarrow$. How would you express does not follow? The only chance I see is $\lnot (A \rightarrow B)$.

 

[Stephen Tashi]

Now, if we include the not we get "it is not the case that if the course was passed, then regular work as done." Is this correct?

Yes, I'd say that's correct. The only question is whether your course materials count it as an answer. Do you know whether your course materials want an answer without a "not" in front of the if-then?

 

[Borg]

The project that I work on has given me some insight on how to answer this.
Don't take this as a serious answer - it's just very similar to the dumb logic that I have to deal with.

If the course was passed and regular work was done, then regular work was done.
If the course was passed and regular work was NOT done, then regular work was NOT done.

If the course was NOT passed and regular work was done, then regular work was done.
If the course was NOT passed and regular work was NOT done, then regular work was NOT done.

 

[FactChecker]

If you really want to have a strict "if ... then" statement, then @LCKurtz answer in #2 is good: if( passed ) then (RegularWorkDone or not RegularWorkDone). In other words, passing implies nothing about regular work.