# English to logic translation

1. Dec 18, 2011

### Syrus

1. The problem statement, all variables and given/known data

I am going back and reviewing some elementary material in logic/set theory. Among the problems in the quantifier section is the following english sentence to logic sentence translation:

Everyone likes Mary, except Mary herself.

Now, my attempt was: (∀x)[(x≠m → L(x,m)) ∧ (x=m → ¬L(x,m))], where m stands for "mary," and L(a,b) stands for "a likes b."

The solution to the exercise in the text was given as: (∀x)(x≠m → L(x,m)). I was a bit skeptical of this and searched the problem online and found another, different solution:
(∀x)(x≠m ↔ L(x,m)).

My question is, which of these three is correct? (or, if they are all/some equivalent, how?)

2. Relevant equations

3. The attempt at a solution

2. Dec 19, 2011

### Syrus

Could anyone at least verify my translation of the following English statement:

If nobody failed the test, then everybody who got an A will tutor someone who got a D.

¬(∃w)F(w) → (∀x)[A(x) → ((∃y)D(y) → (∃z)T(x,z))], where F(x) stands for "x failed the test," A(y) stands for "y got an A on the test," D(z) stands for "z got a D on the test," and T(a,b) stands for "a tutors b."

Last edited: Dec 20, 2011