1. The problem statement, all variables and given/known data A discrete mathematics class contains 1 mathematics major who is a freshman, 12 mathematics majors who are sophomores, 15 computer science majors who are sophomores, 2 mathematics majors who are juniors, 2 computer science majors who are juniors, and 1 computer science major who is a senior. Express each of these statements in terms of quantifiers and then determine its truth value. a) There is a student in the class who is a junior. b)Every student in the class is a computer science major. c) There is a student in the class who is neither a mathematics major nor a junior. d)Every student in the class is either a sophomore or a computer science major. e) There is a major such that there is a student in the class in every year of study with that major. 2. Relevant equations 3. The attempt at a solution First of all, let P(s, c, m) be "student s has class standing c and is majoring in m." I am having trouble with part (c). My answer to this part is [itex]\exists s \exists c \exists m (\neg P(s,c,math) \wedge \neg P(s,junior,m)[/itex] Evidently, the true anser is [itex]\exists s \exists c \exists m (P(s,c,m) \wedge (c ~ \ne ~ junior) \wedge (m ~ \ne ~ math)[/itex] At first I figured what was wrong with my answer was, that P(s,c,math) and P(s,junior,m) spoke about two different students; but then I realized, since both propositional functions assumed the variable s, they must be speaking of a single person at a time. Translating my answer to English, "It is not true that student s has class standing c and is majoring in math, and it is not true that this same student is a junior and is majoring in m," which I imagine would simplify to, and be logically equivalent to, "There is a student in the class who is neither a mathematics major nor a junior." So, is my answer equally valid?