Discrete math Exam 2 Study Guild Questions With 100% Verified Correct Answers.

The set of people who speak English, the set of people who speak English with an Australian accent - correct answer There exist people who speak English without an Australian accent. However everyone who speak English with an Australian accent speaks English. Thus we see that the first set is not a subset of the second, but the second set is a subset of the first. The set of fruits , the set of citrus fruits - correct answer There exist fruits that are not citrus fruits; however, every citrus fruits is a fruit. Thus we see that the first set is not a subset of the second, but the second set is the subset of the first. The set of student studying discrete mathematics, the set of students studying data structures. - correct answer There exist student who are studying discrete mathematics and not studying data structures, and there exist students who are studying data structures and not studying discrete mathematics. Thus we see that neither set is a subset of the other. P(x): x^3 > 1 - correct answer For any integer x, x^3>1 if and only if x>1. Thus we see that the truth set of P(x) is Z^+, the set of positive integers. Q(x) : x^2 = 2 - correct answer There does not exist any integer x such that x^2 = 2 we seet that the turth set of Q(x) is Ø the empty set. R(x) : x< x^2 - correct answer For any integer x, x<x^2 if and only if x^2 > x x^2-x > 0 x(x - 1) > 0 This will be the case if and only if x < 0 or x > 1. The truth set for R(x) is the set of all integers except for 0 and 1. They represent this set is symbolical as Z - {0,1} The set of sophomores taking discrete math at the school - correct answer The set above is the set of the student at the school who are sophomores and who are taking discrete math. Which is A n B. The set of sophomores at your school who are not taking discrete math - correct answer The set described above is the set of student at our school who are sophomores and who are not taking discrete math. Which is A - B The set of student at your school who either are sophomores or taking discrete math. - correct answer The set is AUB The set of student at your school who either are not sophomores or are not taking discrete mathematics - correct answer The set of student who are not sophomores is Ā. The set of student at the school who are not taking discrete math is B̅. ĀUB̅ A U (B n C) = (A U B) n (A U C) - correct answer table A U (B n C) = (A U B) n (A U C) - correct answer Let A = {0,2,4,6,8,10}, B = {0,1,2,34,5,6,}, and C = {4,5,6,7,8,9,10} - correct answer The set A n B n C is the set of all x such that x E A and x E B and x E C. A n B n C = {4,6} A U B U C - correct answer The set A U B U C is the set of all x such that x E A or x E B or x E C. A U B U C = {0,1,2,3,4,5,6,7,8,9,10} (A U B) n C - correct answer The set AUB is the set of all x such that x E A or x E B. Thus is A U B = {0,1,2,3,4,5,6,8,10} Answer: (AUB)nC = {4,5,6,8,10} (A n B) U C - correct answer The set A n B is the set of all x such that x E A and x E B. Thus we see that A n B = {0,2,4,6} Further, the set (A n B) U C is the set of all x such that x E (A n B) or x E C. Thus (A n B) U C = {0,2,4,6,7, 8,9,10} (A n B) U C - correct answer A n B = {0,2,4,6} (A n B) U C = {0, 2,4, 5, 6, 7, 8, 9, 10}