Phil 102 Fall 2004 – Quiz Four Practice Solutions:
Mostly Quantifiers
1.
(i) ¬(Cube(b) ^ Medium(b)) ^ ¬(Large(b)
^ Tet(b))
(ii) Ex(Adjoins(x,c) ^
Dodec(x))
(iii) Cube(c) –>
Ex(Dodec(x) ^ Adjoins(x,c))
(iv)-(vi) I did in class
(vii) There is a small dodecahedron
behind c – oops. I should have used 'BackOf'
(viii) Ey(Small(y) ^
Dodec(y) ^ ¬BackOf(y, c)) equivalently ¬Ay((Small(y) ^ Dodec(y))
–> BackOf(y, c))
(ix) ¬Ey(Small(y) ^
Dodec(y) ^ BackOf(y, c)) equivalently Ay((Small(y) ^ Dodec(y)) –>
¬BackOf(y, c))
(x) AyLarge(y) –> Ax(Cube(x) –> Large(x))
2.
(i) F (ii) F (iii) T (iv)
T (v) F
5. (i) I did in class
(ii) 
(iii) 
(iv) and (v) you should be able to do yourselves – we've had them
before.
(vi) Try proving each of P and Q separately via ¬-Intro. Now use
this proof to prove ¬(P ^ Q)
therefore ¬P v ¬Q
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