Propositional Logic: Edit Protected Wikipedia Entry Only as Admin

[Bashyboy]

Homework Statement

You cannot edit a protected Wikipedia entry unless you
are an administrator. Express your answer in terms of e:
“You can edit a protected Wikipedia entry” and a:“You
are an administrator."

I thought the answer would be a\rightarrow\neg e; but the actual answer is,
e\rightarrow a. Why is that?

 

[HallsofIvy]

"¬e" says "you can NOT edit a protected Wikipedia entry" so "a→¬e" says "if you are an administrator you can NOT edit a protected Wikipedia entry"- not at all what you want to say.

"You cannot edit a protected Wikipedia entry unless you are an administrator" is the same as "If you are not a Wikipedia administrator, you cannot edit a protected Wikipedia entry", ¬a→¬e and that is the same as e→a.

 

[Bashyboy]

All right, I have yet another one:
You can graduate only if you have completed the requirements of your major and you do not owe money to the university and you do not have an overdue library book. Express your answer in terms of g: “You can graduate,” m: “You owe money to the university,” r: “You have com-pleted the requirements of your major,” and b:“You have an overdue library book.”

I wrote my answer to be (r \wedge \neg m \wedge \neg b)\rightarrow g

Yet, the answer key says the answer is the reverse. I don't really understand.

 

[Bashyboy]

Does anyone have any input?

 

[sammycaps]

What do you mean the reverse?

 

[Bashyboy]

g → (r∧¬m∧¬b) like this. Sorry, I can see how that would be confusing.

 

[sammycaps]

It may help to remember that "only if" is not the same as "if". P only if Q means P->Q but P if Q means Q->P. (I *think*)

 

[ImaLooser]

g → (r∧¬m∧¬b) like this. Sorry, I can see how that would be confusing.

That one is tricky. The clue is "only if." a only if b translates as b->a. Your answer could be a true statement, but they weren't looking for a true statement, they were looking for a literal translation.

 

[sammycaps]

That one is tricky. The clue is "only if." a only if b translates as b->a. Your answer could be a true statement, but they weren't looking for a true statement, they were looking for a literal translation.

Did you mean that a only if b translates to a->b?

 

[ImaLooser]

Did you mean that a only if b translates to a->b?

Whoops! You are right. That's what 17 years after grad school will do.