Here's a quick summary for symbolizing English statements into PL.

  1. First a "universe of discourse" is assumed, the set of objects under discussion (e.g., all people in class).
  2. Names are provided, lower case letters from a - u. We might take 'h' to stand for Halpin.
  3. Then predicates and relations are defined, (e.g., we might take 'F' to stand for "is female").
  4. Finally, we use quantifiers, upside-down 'A' and backwards 'E' to stand for "all" and "some" respectively. Along with quantifiers, we'll always use variables: w, x, y, z. For "Someone in class is female" we'll write "There is a person x such that x is female" or (%x)Fx. (If you don't have the logic font installed, the quantifiers will look like '%' and '^'.)

After reading the details just above, think about the examles below:















To say that Halpin is not female, we would write:
To symbolize "there are female members of the class" we could write:
To say (falsely) that everyone is female, we can write:

Now, make sure you understand the summary at the top of the page and answer the following questions:

How would you symbolize "Someone in class is not female"? Answer
How would you symbolize "Halpin's not female but someone in class is"? Answer
Now how would you symbolize "If someone's not female, then not everyone is female"? Answer