Exam 7: Logic, Sets, and Counting

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Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let A = {n ∈ N| n > 50} B = {n ∈ N| n < 250} O = {n ∈ N| n is odd} E = {n ∈ N| n is even} -B \cup E

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Use the Venn diagram to find the requested set: -Find A \cup B.  Use the Venn diagram to find the requested set: -Find A  \cup  B.

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Evaluate: -Evaluate: -

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Use a Venn Diagram and the given information to determine the number of elements in the indicated region: -Use a Venn Diagram and the given information to determine the number of elements in the indicated region: -

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Tell whether the statement is true or false: -3 \in {6, 9, 12, 15, 18}

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One of the following is false; indicate by letter which one:

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Evaluate: -Evaluate: -

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Evaluate: -Evaluate: -

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Construct a truth table to decide if the two statements are equivalent: -~(~q); q

(True/False)
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Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; andU= {1,2,3,4,5,6,7,8} Determine whether the given statement is true or false. -A \subset A

(True/False)
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Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false -{9} \subset A

(True/False)
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Construct a truth table for the proposition: -p  Construct a truth table for the proposition: -p   (p   \Lambda   ~p) (p Λ \Lambda ~p)

(Multiple Choice)
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Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; andU= {1,2,3,4,5,6,7,8} Determine whether the given statement is true or false. -{5} \subseteq D

(True/False)
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Construct a truth table to decide if the two statements are equivalent: -Construct a truth table to decide if the two statements are equivalent: -

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A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with the following results: 90 were interested in an interview show and a documentary, but not reruns. 12 were interested in an interview show and reruns but not a documentary 42 were interested in reruns but not an interview show. 72 were interested in an interview show but not a documentary. 30 were interested in a documentary and reruns. 18 were interested in an interview show and reruns. 24 were interested in none of the three. How many are interested in exactly one kind of show?

(Multiple Choice)
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Construct a truth table to decide if the two statements are equivalent: -~p  Construct a truth table to decide if the two statements are equivalent: -~p   ~q; ~(p    \Lambda   q) ~q; ~(p Λ \Lambda q)

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Construct a truth table for the proposition: -~p \rightarrow (~p Λ \Lambda s)

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Use the Venn diagram below to find the number of elements in the region.  Use the Venn diagram below to find the number of elements in the region.    -n((A  \cap  B)  \cap  C) -n((A \cap B) \cap C)

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Evaluate: -Evaluate: -

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Use the Venn diagram below to find the number of elements in the region. Use the Venn diagram below to find the number of elements in the region.    - -Use the Venn diagram below to find the number of elements in the region.    -

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