Problem 3 (6 points) Consider a fictional world where aliens are trying to infiltrate Earth by posing as humans. NASA has implemented new space travel customs protocols in an attempt to identify them. You are given the following facts: 1. Everyone who entered Earth and who was not a diplomat was searched by a NASA official 2. William was an alien. 3. William entered Earth. 4. William was searched by aliens only. 5. No alien was a diplomat. Show using first-order logic that: Goal: There is an individual who is both an alien and a NASA official. Your solutions should have the same format, syntax, and semantics of First-Order Logic as in the First- Order Logic class session slides. Hints: Start by translating the goal into FOPC and enter it into the line marked "goal". Line numbers 1-5 should be the FOPC statements that are equivalent to the English sentences 1- 5 above. Use only the following predicates: Entered(x) meaning "x entered Earth". Diplomat(x). NASAOfficial(x), Alien(x), and Searched(XJ) meaning that "x searched y". You may introduce any constants or variables that you need. The Reasoning column should contain references to an inference rule and the statements that you used to derive the new sentence. For example, "Existential elimination on 7" or "Modus ponens on 9 and 3" or "And-introduction on 1, 3, and 5" or "de Morgan's rules on 7". Your last line in the table should be the same FOPC statement as your goal. You may or may not need all of the lines in the table. + # FOPC Sentence Reasoning -- GOAL - given given given given given