Symbolization into monadic predicate logic Symbolize the English sentences below, using the abbreviations provided and a domain that is restricted to persons. Please write your answers on a separate sheet of paper (not on this sheet), double-spaced, so that there is room to indicate any errors in your work. Fx: x is a faculty member Gx: x will graduate Hx: x is in the Honors program Jx: x is a junior Lx: x has taken a logic course Mx: x is a math major Ox: x is overworked Px: x is a philosophy major Sx: xis a senior Vx: x has taken a course in yalue theory Wx: x is writing a thesis (1) (2) (3) [3 points] [3 points] [3 points] (4) Everyone who is double-majoring in philosophy and math has taken a logic course unless s/he is Some but not all philosophy majors are in the Honors program Some juniors and seniors have taken a course in value theory All juniors and seniors have taken a course in either value theory or logic. overworked [4 points] (5) Among the philosophy majors, all and only the seniors are writing a thesis [4 points] (6) No philosophy major will graduate unless s/he has taken a course in logic and in value theory [5 points] (7) Some junior philosophy majors are overworked, unless no juniors are overworked.[5 points] (8) Ifa philosophy major is writing a thesis, then s/he is a senior unless s/he is in the Honors program [5 points] (9) If any philosophy major is writing a thesis, then at least one faculty member is overworked. [6 points] (10) Ifall philosophy majors are writing a thesis, then some but not all faculty members are overworked [6 points]