Exam 8: Sets and Logic

Use set notation to identify the shaded portion of the Venn diagram.

Specify the set by description. $\{ 1,2,3,4,5,6 \}$

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. $\overline{A \cap B ) \cap C }$

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

List all subsets of the given set. Identify any of the subsets that are improper. {6, 7, 8, 9}

Answer the question and tell whether it illustrates inductive or deductive reasoning. Give the $50 \text { th }$ number in the pattern: $1,4,9,16,25 , \ldots$ The $50 \text { th }$ number is __________. It illustrates __________ reasoning .

Use Venn diagrams to check the validity of the argument. Some students take math. Some students earn an A. Therefore, some math students earn an A.

List all subsets of the following set. $C = \{ 3,9 \}$

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. $\bar { A } \cup ( B \cap C )$

Draw a conclusion and tell whether it illustrates inductive or deductive reasoning. All dogs have fur. Poodles are dogs. Therefore, poodles ______________.

Consider the following statement. A set is defined to be a collection of objects.

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. $\overline { A \cup ( B \cap C ) }$

Translate the following into set notation. E or F

List all subsets of the given set. Identify any of the subsets that are improper. $\{ 3 \}$

There have been $44$ U.S. presidents. 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 in the Senate and held a cabinet post, but never served as vice-president? __________ president(s)

A poll was taken of $100$ students at a commuter campus to find out how they got to campus. The results were: $43$ said they drove alone. $31$ rode the bus. $27$ rode in a carpool. $9$ used both carpools and rode the bus. $11$ used both a carpool and sometimes drove alone. $6$ used buses as well as drove alone. $4$ used all three methods. How many are not using any of the three (Region VIII)? 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.

Construct a truth table for the statement. ~ ( ~ p ) cellpadding ="0 " cellspacing ="0 " width =62\% " border ="1"> p \simp \sim( \simp)

Let U be the universal set. If $C \subset D$ , describe the following set. $D \cup \bar { C }$ $D \cup \bar { C }$ = __________

In a sample of defective tires, 72 have defects in materials, 95 have defects in workmanship, and 23 have defects of both types. How many tires are in the sample? __________ tires

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