A discrete math class contains 1 math major who is a freshman, 12 math major who

Question

A discrete math class contains 1 math major who is a freshman, 12 math major who are sophomores, 5 computer science major who are sophomores, 2 math majors who are juniors, 2 computer science majors who are juniors, and 1 computer science major who is 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 math 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.

Explanation / Answer

Greetings... We let P(s,c,m) be the statement that student s has class standing c and is majoring in m. The variable s ranges over students in the class, the variable c ranges over the four class standings, and the variable m ranges over all possible majors. The proposition is ?s?mP(s, junior,m). It is true from the given information. The proposition is ?s?cP(s,c,computer science). This is false, since there are some mathematics majors. The proposition is ?x?c?m(P(s,c,m) ? (c? junior) ? (m ?mathematics)). This is true, since there is a sophomore majoring in computer science. The proposition is ?s(?cP(s,c,computer science) ? ?mP(s, sophomore,m)). This is false, since there is a freshman mathematics major. The proposition is ?m?c?sP(s,c,m). This is false. It cannot be that m is mathematics, since there is no senior mathematics major, and it cannot be that m is computer science, since there is no freshman computer science major. Nor can m be any other major. Good Luck!

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