Unit 8 Answers
1.
a) x y L(x, y)
b) x y L(x, y)
c) x y L(x, y)
d) x L(x, George)
e) x y L(y, x)
f) x y L(y, x)
g) x y L(x, y)
2.
a) x ( S(x) y ( B(y) H(x, y) ))
b) x ( S(x) y ( B(y) H(x, y) ))
c) x ( S(x) y ( B(y) H(x, y) ))
d) x ( S(x) y ( B(y) H(x, y) ))
e) x ( B(x) y ( S(y) H(x, y) ))
3.
a) x ( B(x) E(x) )
b) x( ( B(x) E(x) ) G(x) )
c) x ( B(x) G(x) )
d) No.
4.
a) x ( G(x) F(x) )
b) x( Z(x) M(x) )
c) x( M(x) F(x) )
d) x( Z(x) G(x) )
e) Yes. For an arbitray animal x if Z(x), then M(x) by b). Then by c) F(x) holds for that x. Hence from a) by modus tollens G(x) holds.