Modus Ponens 2: More Translation Practice

Hot dog hot dog

Lesson:
1. Review validity.
2. Review translation.
3. Simple proofs.

Translation
Here's how we do a basic conditional translation:

E.g. 1, If you're happy and you know it then clap your hands. = H>C

First write down the first letter of a key word in the antecedent (e.g., 'H' from happy) then write down the symbol '>' and finally write down the first letter of a key word in the antecedent (e.g., 'C' from clap).

Order doesn't matter!
When we translate, the symbol for antecedent always goes first followed by '>', followed by the symbol the consequent.

E.g. 2, Clap your hands if you're happy and you know it. = H>C.

Notice that even though the words of the sentence are ordered differently from e.g., 1, we still symbolize it the same as e.g., 2. Doing so preserves the logical structure. That is, "If you're happy and you know it then clap your hand" and "Clap your hand if you're happy and you know it" both have the same logical structure. To see why, let's look at a similar example but with a different logical structure.

E.g. 3, If you clap your hands then you're happy and you know it. = C>H.
or
E.g. 4, You're happy and you know it if you clap your hands. = C>H.

Notice that e.g. 1 and 2 mean something different than e.g. 3 and 4. If we had translated e.g., 2 as C>H it would mean the same thing as e.g., 3.

Translation Practice
A.

1. If I were a Boy just for a day I'd Roll out of bed in the morning.
2. I'd be Coming right back home to you if I could Fly.
3. If I could Find a way I'd take back those Words that hurt you and you'd stay.
4. You shoulda put a Ring on it if you Liked it.
5. If I Eat too much I feel Tired. 
6. If you Lose yourself in the music, the moment then you Own it, you better never let it go. 
7. You only get one Shot, do not miss your chance to blow if this opportunity Comes once in a lifetime.