Can you help me write the following argument in symbolic form?

This is what I’ve got so far. Any computer science majors out there who can chime in?

Let P = Maria goes out
Let Q = Maria helps Axel with his maths homework
Let R = Axel fails the maths unit
“If Maria does not go out then she will help Axel with his maths homework.” ~P →Q
“Axel will fail the maths unit unless Maria helps him with his maths homework.” (can also be written as “Either Maria helps Axel with his maths homework, or Axel will fail the maths unit.”) Q ˅ R
“Therefore if Maria goes out, Axel will fail the maths unit.” P → R

~P → Q
Q ˅ R
P
————-
R

I am not a computer science major, but I am a philosopher. We invented symbolic logic, and we all have to learn it.

What you have looks mostly correct. “Unless” can be translated as “if not,” but you can also use disjunction (aka “or”) as you have. So “Axel will fail the maths unit unless Maria helps him with his maths homework” could be translated either as Q v R or ~Q → R. Notice that the argument has a conditional conclusion, so you don’t need to end up with an atomic sentence at the end of the problem. Therefore, your symbolic representation of the argument should be:

~P → Q
Q ˅ R
————
P → R

Alternatively, it could be:

~P → Q
~Q → R
————-
P → R

Since you don’t know whether or not Maria will go out, you cannot reach any conclusion about whether or not Axel will fail the maths unit. (So not only don’t you need to end up with an atomic sentence at the end of the problem, you cannot do so with the information provided.)

I agree that no conclusion can be drawn, but my reasoning is different. We have ~P → Q. We can say that if P is false and therefore ~P is true then Q is true. However, we are told that P is true and therefore ~P is false. We cannot conclude anything about Q. In the real world, it would seem reasonable to suppose that if Maria goes out she will not be able to help Alex, but that is not explicitly given in the statement of the problem.

@LostInParadise Nothing in the statement of the problem tells us that P is true. The real problem is that the argument is invalid.

We are told to show P->R and we are not given any values for P, Q or R. That being the so, for P->R to be true, it must be the case that when P is true then R must be true. We therefore only need to consider the case when P is true and see if R follows, which it does not.

@LostInParadise “We are told to show P->R”

No, we aren’t. We were asked to symbolize the argument. And since the argument is invalid, we wouldn’t be able to show that P → R from the premises given. In any case, I was responding to this statement that you made:

“However, we are told that P is true and therefore ~P is false.”

This is false. We are not told that P is true. We have no information about the truth of P, Q, or R.

@SavoirFaire , We are in agreement. My statement that P is true was a bit of sloppiness. What I should have said was that to determine if P->R we posit that P is true and see if that leads to R being true.