Write your proofs clearly using complete sentences. Try silently reading what you've written and decide if any words are missing. if you introduce new notation or variable names, state explicitly what they represent. Don 't use any symbols such as => or V in your proofs; use words instead. It is allowed and encouraged to work with your classmates on these problems, but your submission must be entirely your own work. Solutions which are copied from a student or another source will receive a score of 0. 1. Suppose that \"Girls like cats\" and \"Boys like dogs\" are true statements and that \"Everybody likes horses" is a false statement. Which of the following are true? Hint: Label each of the given statements, and think about each of the following using connec- tives. a. If girls like cats, then everybody likes horses. b. If everybody likes horses. then boys like dogs. c. If everybody likes horses, or girls like cats, then boys like dogs. d. If boys like dogs and girls like cats, then everybody likes horses