Beginner: Library BooksSample answers

This could be written using a function, “major” for instance, mapping people to their subjects of study, but that would make it a little more awkward to represent the constraints so here the relationship between pupils and subjects has been defined the other way around.

By nesting one function symbol inside another, we are able to refer to the number of books on loan to the student of French, for example, without needing to use ∀ or ∃ or any connectives.

Note the use of the logical symbol “∃”, which abbreviates the keyword “SOME”. This is used to say that some (i.e. at least one) object of a given sort has a given property. It binds a variable, in the same way as ALL. Here we want to say there is not an individual satisfying the condition, so the SOME expression is negated. Of course, we could equivalently have written “∀ x (loans(x) < 15)” in this case.

One more detail: note that the empty braces after the declaration of the function symbol “loans” have been replaced by a dot. Nothing hangs on this: it just makes things look a bit less messy. Take care with it, though, because if you write the dot and then add the curly braces after it, you will get a (possibly obscure) syntax error!