Exam 2: The Basic Concepts of Set Theory

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. - $n \left( A ^ { \prime } \right) = 26 , n ( B ) = 32 , n ( A \cap B ) = 11 , n \left( A ^ { \prime } \cup B ^ { \prime } \right) = 35$

Determine whether the sets are equal, equivalent, both, or neither. - $\{ x \mid x$ is an even integer $\}$ and $\{ x \mid x$ is an odd integer $\}$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $7.....\{ 4,20,5,7,12 \}$

For the given sets, construct a Venn diagram and place the elements in the proper region. -Let $\mathrm{U}=\{1,2,3,4,5,6,7,8\}$ $A=\{3,6,8\}$ $B=\{4,6\}$ $C=\{1,6,7,8\}$

The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. soybeans (s) soybeans (s) soybeans (s) peanuts (p) rice (r) sugarcane (n) corn (c) cotton (t) rice (r) hay (h) hay (h) corn (c) wheat (w) wheat (w) cotton (t) Let U be the smallest possible universal set that includes all of the crops listed, and let A, K and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find each of the following sets. -The set of crops in both A and K

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $a ..... \{ A , B , C , \ldots , Z \}$

Show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of itself. Be sure to show the pairing of the general terms in the sets. - $\{ 3,5,7,9 , \ldots \}$

Describe the conditions under which the statement is true. - $A \cup B = B$

Write a description of the shaded region using the symbols A, B, C, $\cup$ , $\cap$ , -, and ' as needed. -

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. - $n ( A ) = 48 , n \left( B ^ { \prime } \right) = 60 , n ( C ) = 51 , n ( A \cap B ) = 20 , n ( B \cap C ) = 19 , n ( A \cap C ) = 18 \text {, }$ $\mathrm { n } ( \mathrm { A } \cap \mathrm { B } \cap \mathrm { C } ) = 12 , \mathrm { n } ( \mathrm { A } \cup \mathrm { B } ) = 70$

Shade the regions representing the set. - $\left( A \cup B \cup C ^ { \prime } \right) ^ { \prime }$

Solve the problem. -A survey of a group of 112 tourists was taken in St. Louis. The survey showed the following: 63 of the tourists plan to visit Gateway Arch; 44 plan to visit the zoo; 9 plan to visit the Art Museum and the zoo, but not the gateway Arch; 14 plan to visit the Art Museum and the Gateway Arch, but not the zoo; 16 plan to visit the Gateway Arch and the zoo, but not the Art Museum; 7 plan to visit the Art Museum, the zoo, and the Gateway Arch; 14 plan to visit none of the three places. How many plan to visit the Art Museum only?

Write a description of the shaded region using the symbols A, B, C, $\cup$ , $\cap$ , -, and ' as needed. -

Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words. - $( A \cap B ) \cap C ^ { \prime }$

Decide whether $\subset$ , $\subseteq$ , both, or neither can be placed in the blank to make a true statement. - $\{ s , r , t \} \ldots \{ s , r , t \}$

Tell whether the statement is true or false. - $\{ 8 \} = \{ x \mid x \text { is an even counting number between } 10 \text { and } 16 \}$

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $\left( A ^ { \prime } \cup C \right) \cap B ^ { \prime }$

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $\left( A \cap B ^ { \prime } \right) \cup \left( B \cap A ^ { \prime } \right)$

Find the Cartesian product. - $\mathrm { A } = \{ \mathrm { i } , \mathrm { a } \}$ $\mathrm { B } = \{ \mathrm { t } , \mathrm { d } , \mathrm { m } \}$ Find $\mathrm { A } \times \mathrm { B } .$

Find the cardinal number of the set. - $\{ x \mid x$ is an even integer number smaller than $100 \}$