Discussion
Consider the following pairings in first order logic.
Universal quantifier - naturally paired with implication
Existential quantifier - naturally paired with conjunction
Function symbol - denotes an object
Predicate symbol - denotes an object
How many of the pairs given above are correctly matched?
Answer: C
The first three are correct. A predicate denotes a relation and yields a truth value, whereas a function denotes an object and may appear wherever a term is expected. The distinction determines where each may legally appear in a formula, and confusing them produces expressions that are not well formed at all rather than merely false, which is at least an error that a parser will catch.
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