Question 9) Symbolize the following valid argument and prove its validity in our proof system. UD: Everything If BLACK holes exist, then some PARTS of the universe are SINGU LARITIES. Now, Jean-? Picard REFUSE82 to go near parts of the universe that are singularities. So, if Powehi is a black hole, then there is some part of the universe to which Jean-Luc Picard refuses to go. Symbols to copy/ paste (if you wish to type your answers): av—-&V—><—>J_.'. Am“.

Question 8 Consider the following argument. Every STUDENT LIKES, some COURSES. Everyone WRITING this quiz is a student. So, if Ganlin is writing this quiz, then there is a course that Ganlin likes. If we let the universe of discourse be the set of all things, the argument can be formalized thusly: (X73 x X)) XE - BM: (XS + XM) XA '((ATX x8 AD) < XS) LEXA Symbols to copy/paste (if you wish to type your answers): B IJAY A TX E V VX .. AT 1 12pt V Paragraph X

Question 7 Using the interpretation below, translate the following FOL statements into English. UD: Chess pieces on a chess board Rx: x is a rook. Bx: x is a bishop. Px: x is a pond. Wx: x is white. Kx: is a knight. xFy: x is in front of y. Ax: x is black. xLy: x is left of y. Qx: X is a queen. xRy: x is right of y. 1. Vx [Rx -> By(Py & xLy)] 2. 3x [(Ax & Bx) & Vy((Wy & Ky) -> xFy)] 3. VxVy [(Qx & Ry) -> -(xLy v xRy)]

Question 6 6 pts Translate the following English statements into FOL. Please note that every capitalized word stands for a unique predicate or relation. Symbols to copy/paste (if you wish to type your answers): 3V- &V-91.. UD: People 1. There is a GIRL that every BOY LIKES2. 2. No BOY is FUNNIER than any GIRL. 3. Sam is a SMART GIRL who everybody likes. 4. Only those who FORGIVE are HAPPY. 5. No SMART person would VOTE for Donald Trump. 6. Any person, either MUSLIM, CHRISTIAN, or JEWISH, should TOLERATE, Donald Trump. HTML E

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