T4: 5 of 9

Again, we can use lower case letters as names of our symbolic languge (though we won't use 'v' because that's used as a connective and we won't use 'w','x','y' or 'z' as names because these will be used as variables).

And we use upper case letters (except for 'V') as predicates OR as whole sentences.

So, the upper case letters can be used in different ways. In fact, there's yet another way they can be used: as relation symbols. For example, we could take 'L' to stand for the loves relationship. Then

Agnes loves Bob

would be symbolized as


It should be clear that, before doing any symbolizing, we need to be very clear about which symbols stand for what things, properties, or relationships. We'll do this by giving an interpretation of our symbolic language.

For example, to say that 'L' stands for the loves relationship, we'll write

Lxy: x loves y

What's x? who's y? Just take them to be placeholders. When you symbolize, you'll fill in for 'x' and 'y' with names (like 'a' and 'b'). In fact, it's time to try some. Here's a first symbolization exercise for you!

Symbolize  Using the '>' symbol for horseshoe, the '=' symbol for the triple-bar, fill in the following fields (the blank boxes) with an approprite sentence from our symbolic language... You'll need to type in an answer in a field, then press TAB. Your answer will be checked immediately.

a: Agnes, b: Bob
Wx: x will go to law school
Mx: x will be miserable
Lxy: x loves y


  1. Agnes will attend law school. (hint)
  2. Agnes and Bob will both attend law school. (hint)
  3. If Agnes will attend law school then so will Bob. (hint)
  4. Agnes loves Bob.
  5. If Agnes loves Bob then Bob loves Agnes.
  6. Bob loves himself but will nevertheless attend law school. (hint)
  7. Either Agnes will attend law school or Bob will not. (hint)