Meaning of realization in Math logic

Question

So I'm reading "A Mathematical introduction to logic" by Herbert.E.enderton.

In the chapter on sentential logic, it used a phrase "Boolean function realized by a wff, $\alpha$"

So I'm abit confused, what exactly do we mean by "wff $\alpha$ realizes a Boolean function"

If a concrete example can be given, that would be so much help.

Answer 1

A Boolean function is any function that takes in a number of truth-values, and returns a truth-value. So, for example, suppose we have a function that takes the truth-values of A, B, and C, and that returns True whenever at least two of these are True (and otherwise returns False) Then we can use the following wff to 'realize' that function:

$(A \land B) \lor (A \land C) \lor (B \land C)$

Of course, there are other wff's that realize that same function. They would all be considered equivalent.