Translate Phrase to Symbolic Logic

Question

Either I am going home or I am not going home. Since if I play basketball, then I’m going home. And, if I don’t play basketball, then I am not going home. And, either I am going to play basketball, or I am not going to play basketball.

I need help getting this translated to symbolic form.

Answer 1

The general idea for this sort of translation to symbolic logic is to pick out which parts are propositions (roughly statements that might be true or false) and which parts are logical operators (e..g and, not, or, if/then). So in this case, we have the following propositions:

I am going home

I play basketball

That's it! Notice that what's stated are just ways of combining those propositions with logical operators. Different books/approaches have different methodologies for turning this into symbolic form. Here's one way, where we don't assign the propositions any symbols:

Either I am going home or I am not going home would be translated to

(I am going home) OR NOT(I am going home).

Depending on your book, you might use different logical symbols for OR or NOT. One common gloss is

OR is represented by v

NOT is represented by ~

So using that translation, this would become

(I am going home) v ~(I am going home)

Your course may prefer that you substitute capital letters for the propositions. Maybe

P for "I am going home"

Q for "I play basketball"

Then we'd get

P v ~P

"if I play basketball, then I’m going home" is an if/then statement, often symbolized with ->. So we'd get

Q -> P

"f I DON'T play basketball, then I am NOT going home" becomes

~Q -> ~P

Either I am going to play basketball, or I am not going to play basketball becomes

Q v ~Q