 
Summary: G53KRRE1
Answers G53KRR 200910
1. (a) Express the following sentences in firstorder logic, using unary predicates Fragile,
Break, Fall, TennisBall.
S1 Fragile things break if they fall (2 marks)
S2 Tennis balls are not fragile (2 marks)
S3 Tennis balls don't break if they fall (2 marks)
Answer
S1 x(Fragile(x) Fall(x) Break(x))
S2 x(TennisBall(x) ¬Fragile(x))
S3 x(TennisBall(x) Fall(x) ¬Break(x))
(b) Give a definition of logical entailment for firstorder logic, that is, what it means
for a set of sentences S to logically entail a sentence A. (4 marks)
Answer S logically entails A if for every interpretation I, if I makes true all sen
tences in S, it also makes A true.
(c) Do sentences S1 and S2 logically entail S3? Justify your answer: if you answered
yes, show why the entailment holds, if you answered no, give a counterexample
interpretation. (10 marks)
Answer No, S1 and S2 do not logically entail S3. An interpretation which satisfies
S1 and S2 but not S3 would be for example where all things break when they
