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.