(1) (10 points) Translate the following sentences into predicate logic. Preserve as much of the structure as possible, and in each case, give the key....

(1) (10 points) Translate the following sentences into predicate logic. Preserve as much of the structure as possible, and in each case, give the key. (For examples of problems like this, see Gamut vol. 1 Exercise 1 p. 69 with solutions on pp. 241-242). It is okay to assume that you are using a =Anne, b =Bill, and c =Claire in the key, so that you do not have to explicitly say this in your key; although if you deviate from this assumption, please indicate as much in your key.

(a) Anne trusts Claire and Claire trusts Bill. But Anne does not trust Bill.

(b) Anne is better at chess than Bill only if Anne is better at chess than Claire. But Anne is not better at chess than Claire. So, Anne is not better at chess than Bill.

(c) Anne trusts Bill if and only if Bill trusts Anne. But Bill does not trust Anne. Therefore, Anne does not trust Bill.

(d) Anne admires Claire and Bill admires Claire. But Claire does not admire herself.

(e) Anne does not respect Bill and she does not trust Bill. Claire does not trust Anne, but she respects Anne.