Exam 8: Sets and Logic

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

Which of the given Venn diagrams highlights the region corresponding to the set of $A \cap B$ ?

Specify the set by description. $\{ 101,102,103 , \ldots , 184 \}$

Use Venn diagrams to check the validity of the argument. Some beautiful women are blond. Blonds have more fun. Therefore, some beautiful women have more fun. __________ ( valid / not valid )

A poll was taken of $100$ students at a commuter campus to find out how they got to campus. The results were: $42$ said they drove alone. $31$ rode the bus. $29$ rode in a carpool. $5$ used both carpools and rode the bus. $10$ used both a carpool and sometimes drove alone. $9$ used buses as well as drove alone. $2$ 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. __________ students

List all subsets of the following set. K = {6, 7, 8, 9}

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

Find the truth value when p is T and q is F. $p \wedge \sim q$

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

Let U be the universal set. If $A \subset B$ , describe the following set. $A \cup B$ $A \cup B$ = __________

List the set in roster form. $\{ x \mid x \in N , x \neq 3$ }

Choose the negation of the statement. No workers get a raise.

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. $31$ rode the bus. $29$ rode in a carpool. $9$ used both carpools and rode the bus. $10$ used both a carpool and sometimes drove alone. $4$ used buses as well as drove alone. $2$ used all three methods. How many are B only (Region II)? 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.

Consider the sets. $A =$ {letters in the word pen } $B =$ $\{ p , i , v \}$ $\mathrm { C } =$ {4} $D =$ $\{ 2 + 1 \}$ $E =$ {three} $F = \{ 3 \}$ What is the cardinality of each set? $| A | =$ __________ $| B | =$ ___________ $| C | =$ ________ $| D | =$ __________ $| E | =$ ___________ $| F | =$ ____________

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

Specify the set by roster. {even counting numbers less than 12}

List all subsets of the given set. Identify any of the subsets that are improper. $\{ Z , m \}$

List all subsets of the following set. $G = \varnothing$

List the set in roster form. $\{ x \mid x \in W , x \leq 6$ }

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