程序代写代做代考 Logic Tutorial 6

Logic Tutorial 6

Predicate Logic Tutorial 3

1.

i) Which of the following are correct formalisations of the following statement:
“Bankers and estate agents are unpopular”?

a. X (banker(X)  estate_agent(X)  unpopular(X))

b. X (banker(X))  (estate_agent(X)  unpopular(X))

c. X (banker(X)  estate_agent(X)  unpopular(X))

d. X (banker(X)unpopular(X))  X (estate_agent(X)unpopular(X))

ii) Show |- cd, where c and d refer to the 3
rd

and 4
th

wffs above.

2. Prove the following:

a. X (p(X)  q(X)  r(X)) |- X (p(X)  q(X))  X (p(X)  r(X))

b. X (p(X)  (q(X)  r(X))) |- X (p(X)  q(X) r(X))

c. X (p(X) ¬q(X)), p(a), Y(q(Y)  s(Y)) |- s(a)

d. X (p(X)  m(X)  n(X)), X (m(X)  Yq(X, Y)) , X (n(X)  Yq(X, Y)),

p(a) |- Yq(a, Y)