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*Type(sleeps) = <math>\langle e,t\rangle</math>
*Type(every) = <math>\langle\langle e,t\rangle,\langle \langle e, t\rangle, t\rangle\rangle</math>
*Type(every boy) = <math>\langle\langle e,t\rangle,t\rangle</math>
and so we can see that the generalized quantifier in our example is of type <math>\langle\langle e,t\rangle,t\rangle</math>
Thus, every denotes a function from a ''set'' to a function from a set to a truth value. Put differently, it denotes a function from a set to a set of sets. It is that function which for any two sets ''A,B'', ''every''(''A'')(''B'')= 1 if and only if <math>A\subseteq B</math>.
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