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 maior 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 (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]