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 |- cd, 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)