Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

English to logic translation

  1. Dec 18, 2011 #1
    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. jcsd
  3. Dec 19, 2011 #2
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook