Formal Method Logic Exercises PDF

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Summary

Symbolise each of the following sentences, using the following symbolisation key: John visited the Eiffel Tower on Monday and the Parthenon on Wednesday. V(j,e,m)&V(j,p,d) If Harry visited the Eiffel Tower on Wednesday, then John visited it on Tuesday. V(h,e,w) → V(j,e,t) Either John visited...

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Symbolise each of the following sentences, using the following symbolisation key:

1. John visited the Eiffel Tower on Monday and the Parthenon on Wednesday. V(j,e,m)&V(j,p,d) 2. If Harry visited the Eiffel Tower on Wednesday, then John visited it on Tuesday. V(h,e,w) → V(j,e,t) 3. Either John visited the Tower of London on Monday or Harry did. V(j,l,m) v V(h,l,m) 4. On Monday, John visited the Eiffel Tower and Harry visited both the Parthenon and the Tower of London. V(j,e,m)& (V(h,p,m)&V(h,l,m)) 5. Harry visited the Parthenon on either Monday or Tuesday and the Tower of London on Wednesday. (V(h,p,m) v V(h,p,t)) & V(h,l,d)

6. John visited Harry on Monday and the Eiffel Tower on Wednesday. V(j,h,m)&V(j,e,d) 7. If John visited the Parthenon on either Monday or Tuesday, then he and Harry both visited the Tower of London on Wednesday.

(V(j,p,m) v V(j,p,t)) → (V(j,l,d) & V(h,l,d)) 8. Harry didn't visit the Tower of London on Monday or Tuesday. ¬V(h,l,m) v ¬V(h,l,t)

9. If Harry didn't visit the Parthenon on either Monday or Tuesday, then he visited the Parthenon on Wednesday, and either the Tower of London or The Eiffel Tower on Monday. (¬V(h,p,m) v ¬V(h,p,t)) → V(h,p,d) & (V(h,l,m) v V(h,e,m)

10. Harry visited neither the Eiffel Tower nor the Parthenon on Tuesday, but he visited the Tower of London on Monday. (¬V(h,e,t) & ¬V(h,p,t)) & V(h,l,m)

Symbolise each of the following sentences, using the symbolisation key from the previous exercise, plus the following:

1. (∃x) S(x) 2. P(x) → !H(x) 3. H(x) → !P(x) 4. S(x) → !T(x,b) 5. V(b, H(y), t) 6. V(x,l,m)&V(x,l,t) 7. V(x,l,m)&V(x,p,d) 8. !T(P(x), H(y)) 9. T(s,d) →V(s,l,m)&V(d,l,m) 10. (S(s)) | (T(x,s) & S(x))...