Exam 8: Sets and Logic

Specify the set by roster. {Counting numbers greater than $152$ }

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{7,9\} C=\{2,7,8,9,10\} List all the members of the set. $\bar { A } \cap ( B \cup C )$

A poll was taken of $100$ students at a commuter campus to find out how they got to campus. The results were: $41$ said they drove alone. $30$ rode the bus. $28$ rode in a carpool. $6$ used both carpools and rode the bus. $9$ used both a carpool and sometimes drove alone. $8$ used buses as well as drove alone. $4$ used all three methods. How many are A and C, but not B (Region IV)? A = {people who drive alone} B = {people who ride the bus} C = {people who carpool} Use the figure (with Regions I to VIII) to answer the question.

Santa Rosa Junior College enrolled 29,000 students in the fall of 2010. It was reported that of that number, 58% were female and 42% were male. In addition, 62% were over the age of 25. How many students were there in each category?

Give the numbers of elements in the regions marked I, II, III, IV, V, VI, VII, and VIII in the figure. $| U | = 2,100 , | A | = 153 , | B | = 812 , | C | = 296 , | A \cap B | = 87$ $| A \cap C | = 94 , | B \cap C | = 58 , | A \cap B \cap C | = 33$ I: __________ element(s) II: __________ element(s) III: __________ element(s) IV: __________ element(s) V: __________ element(s) VI: __________ element(s) VII: __________ element(s) VIII: __________ element(s)

Let $P = \{ U . S \cdot \text { presidents } \} , \quad O = \text { Obama, } W = \text { Washington, } J = \text { Jones }$ . $O \notin P$

How many subsets are there in a set with $r$ elements?

List all subsets of the given set. Identify any of the subsets that are improper. $\{ b , e , h \}$

Which conclusion is valid? No Lizards have fur. Puff has fur.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{7,9\} C=\{2,7,8,9,10\} List all the members of the set. $A \cap ( \bar { B } \cup C )$

Does the B.C. cartoon illustrate inductive or deductive reasoning? Explain your answer.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{3,7\} C=\{2,3,6,7,10\} List all the members of the set. $A \cap \overline { B \cup C }$

Tell whether you believe that the conjecture is true or false. The product of an even number of negative numbers is positive.

Tell whether you believe that the conjecture is true or false. The product of two even numbers is even.

Give the numbers of elements in the regions marked I, II, III, and IV in the figure. $| U | = 1,000 , | A | = 550 , | B | = 425 , | A \cap B | = 75$ I: __________ elements II: __________ elements III: __________ elements IV:__________ elements

Let $N = \{ 2,3,4,5 \} , \quad S = \{ \text { whole numbers between } 1 \text { and } 6 \} , L = \{ a , b , c , d \}$ N = S

Let $P = \{ U . S \cdot \text { presidents } \} , \quad O = \text { Obama, } W = \text { Washington, } J = \text { Jones }$ . $W \in P$

The fire department wants to send booklets on fire hazards to all teachers and homeowners in town. How many booklets does it need, using these statistics? $49,000$ homeowners $5,000$ teachers $4,000$ teachers who own their own homes __________ booklets

At the time of Barack Obama s presidency, there have been 44 presidents of the United States. In order to help you answer the question below, draw a Venn diagram showing the following facts about where each served before assuming the presidency. $14$ were vice-president. $6$ were VP and served in the Senate. $16$ served in the Senate. $2$ were VP and held a cabinet post. $8$ held a cabinet post. $4$ served in the Senate and held a cabinet post. $1$ was VP, in the Senate, and held a cabinet post. How many presidents served as VP and held a cabinet post but did not serve in the Senate?

Construct a truth table for the statement. cellpadding ="0" cellspacing ="0" width ="62\%" border ="1"> pqp\veeq