Problem:
You have now learned how to construct translations, create well-formed formulas, and identify the main operator. Now I would like you to demonstrate your understanding and also help out your classmates if they are having difficulties. Here are the atomic sentences: Calvin wears a hat (C) Hobbes wears mittens (H) Bill went to the store (B) Translate the following sentences into symbolic form using the atomic sentences identified above. Make sure to identify the main operator and, if you disagree with a classmate, defend your translation. Calvin wears a hat but Bill went to the store. Hobbes does not wear mittens but Calvin wears a hat. Bill went to the store and Hobbes did not wear mittens. Neither Hobbes wears mittens nor does Calvin wear a hat. It is not the case that both Calvin wears a hat and Hobbes wears mittens, although Bill went to the store. Hobbes wears a hat and Calvin wears mittens, and in addition Bill went to the store. Calvin does not wear a hat and Hobbes does not wear mittens, but Bill went to the store or Hobbes did wear mittens. Bill did not go to the store, or Hobbes wears mittens and Calvin does not wear a hat. Either Bill did not go to the store or Hobbes wears mittens, and Calvin does not wear a hat. Neither Bill goes to the store nor Hobbes wears mittens, and Calvin wears a hat.