The limitations of HTML (the language used for these hypertext pages) calls for certain adjustments in showing a conventional notation. We will use the following:
PN -- ~P
PQA -- P&Q
PQB -- P <-> Q
PQC -- P->Q
PQO -- PvQ
PQON -- ~(PvQ)
PQARO -- (P&Q)vR
PQRAO -- Pv(Q&R)
FV -- (x)Fx
FW -- (Ex)Fx Usually the E is printed backwards
FGD -- (x)(Fx->Gx)
FGE -- (Ex)(Fx&Gx)
In working with multiple quantifiers (essential when we have two-place predicates), we need to make sure that any variable is properly bound to the correct quantifier. Use the following models as templates, given a code in which F stands for being rich, G for being famous, H for being a friend. Let Fxy represent x having y and Gxy represent x knowing y.
Everyone famous has some friends who are rich:
(x)[Gx->(Ey)(Fy&Hy&Fxy)]
Some who are rich know everyone who is famous.
(Ex)[Fx&(y)(Gy->Gxy)]
Only rich people have famous friends.
(x)(y)[(Gy&Hy&Fxy)->Fx]
We can also talk in a most limited way about how many items we have by using the identity symbol =.
Everyone famous has at least two friends.
(x)[Gx->(Ey)(Ez)(Hy&Hz&Fxy&Fxz& ~y=z)]
There are just two people who are both rich and famous.
(Ex)(Ey)[Fx&Fy& ~x=y &(z)(Fz->z=x v z=y)]
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