Question

Translate each of the following sentences into a formula of propositional logic. Represent each simple sentence by a propositional letter, and state the simple sentence that each propositional letter denotes. When in doubt, make the simple sentences as simple as possible, using logical connectives and negation whenever possible. If a sentence is ambiguous, state this and choose one interpretation for your translation.

a) Orvendil marries the king's daughter, but Fengi does not.
b) Although success is prized by all, yet honor is not.
c) Amleth is suspicious, or Geruth is in mourning and Jutland is peaceful.
d) Amleth is suspicious or Geruth is in mourning, and Jutland is peaceful.
e) John will finish his homework if the wireless router is working and Mary goes to her office.

Answer 1

To translate each sentence into a formula of propositional logic, you can represent each simple sentence by a propositional letter and state the simple sentence that each propositional letter denotes. The translations for the given sentences are provided.

Step-by-step explanation:

a) Let P represent Orvendil marries the king's daughter and Q represent Fengi does not marry the king's daughter. The sentence can be represented as P and not Q.

b) Let R represent success is prized by all and S represent honor is not prized. The sentence can be represented as R but not S.

c) Let T represent Amleth is suspicious, U represent Geruth is in mourning, and V represent Jutland is peaceful. The sentence can be represented as T or (U and V).

d) Let T represent Amleth is suspicious, U represent Geruth is in mourning, and V represent Jutland is peaceful. The sentence can be represented as (T or U) and V.

e) Let W represent John will finish his homework, X represent the wireless router is working, and Y represent Mary goes to her office. The sentence can be represented as W if (X and Y).