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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. Expressing "Every student in the class is either a sophomore or a computer science major." in terms of quantifiers, by letting 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. Which of the following is correct? The proposition is vs(3c P (s, c, computer science) v am P(s, sophomore,m)). This is false, since there is a freshman A mathematics major. The proposition is amvcas P (s, c,m). This is false. It cannot be that m is mathematics, since there is no senior B) mathematics major, and it cannot be that m is computer science, since there is no freshman computer science major. Nor, of course, can m be any other major. The proposition is asacam(P(s, c,m) ^ (c = junior) ^ (m = mathematics)). This is true, since there is a sophomore majoring in computer science.

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. Expressing "Every student in the class is either a sophomore or a computer science major." in terms of quantifiers, by letting 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. Which of the following is correct? The proposition is vs(3c P (s, c, computer science) v am P(s, sophomore,m)). This is false, since there is a freshman A mathematics major. The proposition is amvcas P (s, c,m). This is false. It cannot be that m is mathematics, since there is no senior B) mathematics major, and it cannot be that m is computer science, since there is no freshman computer science major. Nor, of course, can m be any other major. The proposition is asacam(P(s, c,m) ^ (c = junior) ^ (m = mathematics)). This is true, since there is a sophomore majoring in computer science.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. Expressing "Every student in the class is either a sophomore or a computer science major." in terms of quantifiers, by letting 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. Which of the following is correct? The proposition is vs(3c P (s, c, computer science) v am P(s, sophomore,m)). This is false, since there is a freshman A mathematics major. The proposition is amvcas P (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, of course, can m be any other major. The proposition is asacam(P(s, c,m) ^ (c = junior) ^ (m = mathematics)). This is true, since there is a sophomore majoring in computer science. none of the choices
Transcribed Image Text: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. Expressing "Every student in the class is either a sophomore or a computer science major." in terms of quantifiers, by letting 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. Which of the following is correct? The proposition is vs(3c P (s, c, computer science) v am P(s, sophomore,m)). This is false, since there is a freshman A mathematics major. The proposition is amvcas P (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, of course, can m be any other major. The proposition is asacam(P(s, c,m) ^ (c = junior) ^ (m = mathematics)). This is true, since there is a sophomore majoring in computer science. none of the choices
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