Exam 2: The Basic Concepts of Set Theory

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. - $\left\{ \frac { 4 } { 9 } , \frac { 5 } { 9 } , \frac { 6 } { 9 } , \frac { 7 } { 9 } , \ldots \right\}$

List the elements in the set. - $\{ x \mid x$ is an integer greater than $0 \}$

A one-to-one correspondence between the set of counting numbers and the given set has been established. Find an expression for the nth term of the given set that corresponds to the counting number n. -

A one-to-one correspondence between the set of counting numbers and the given set has been established. Find an expression for the nth term of the given set that corresponds to the counting number n. -

Find the cardinal number of the set. -{m, i, s, s, i, s, s, i, p, p, i}

Tell whether the statement is true or false. -{52, 53, 52, 53} = {52, 53}

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $- 8 , \{ 8,10,12 , \ldots , 20 \}$

Determine whether or not the set is well defined. - $\{ x \mid x$ is a low-fat ice cream $\}$

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

Determine whether or not the set is well defined. - $\{ x \mid x$ is a football team that has won the Super Bowl $\}$

Find n(A)for the set. - $A = \{ x \mid x$ is a number on a clock face $\}$

Find n(A)for the set. - $A = \left\{ \frac { 1 } { 2 } , - \frac { 1 } { 2 } , \frac { 2 } { 3 } , - \frac { 2 } { 3 } , \frac { 3 } { 4 } , - \frac { 3 } { 4 } , \ldots , \frac { 19 } { 20 } , - \frac { 19 } { 20 } \right\}$

Decide whether the given statement is always true or not always true. - $\mathrm { A } \cap \mathrm { A } ^ { \prime } = \varnothing$

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find $n \left( A ^ { \prime } \cap B ^ { \prime } \cap C \right)$

Solve the problem. -A local television station sent out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 800 responses with the Following results: 240 were interested in an interview show and a documentary, but not reruns. 32 were interested in an interview show and reruns but not a documentary. 112 were interested in reruns but not an interview show. 192 were interested in an interview show but not a documentary. 80 were interested in a documentary and reruns. 48 were interested in an interview show and reruns. 64 were interested in none of the three. How many are interested in exactly one kind of show?

Decide whether the given statement is always true or not always true. - $( \mathrm { A } \cap \mathrm { B } ) ^ { \prime } = \mathrm { A } ^ { \prime } \cup \mathrm { B } ^ { \prime }$

Determine whether the sets are equal, equivalent, both, or neither. -{brake} and {break}

Tell whether the statement is true or false. -{4, 17, 23, 10, 36} = {36, 17, 10, 32, 4}

Let A and B be sets with cardinal numbers, n(A)= a and n(B)= b, respectively. Decide whether the statement is true or false. - $n ( A - B ) = n ( B - A )$

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