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Problem 12
State whether the statements are true or false. $$ \text { a. }\\{Q\\}=\varnothing $$
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suppose \(A \subset B\) and \(B \subset C\), where \(A\) and \(B\) are any two sets. What conclusion can be drawn regarding the sets \(A\) and \(C ?\)
Determine whether the pairs of sets are disjoint. a. \(\varnothing,\\{1,3,5\\}\) b. \(\\{0,1,3,4\\},\\{0,2,5,7\\}\)
Let \(A, B\), and \(C\) be subsets of a universal set \(U\) and suppose $n(U)=100, n(A)=28, n(B)=30\(, \)n(C)=34, n(A \cap B)=8, n(A \cap C)=10, n(B \cap C)=15$ and \(n(A \cap B \cap C)=5\). Compute: a. \(n(A \cup B \cup C)\) b. \(n\left(A^{c} \cap B \cap C\right)\)
Use Venn diagrams to illustrate each statement.. $$ A \cap(B \cap C)=(A \cap B) \cap C $$
Let \(A=\\{1,2,3\\} .\) Which of the following sets are equa to \(A\) ? a. \(\\{2,1,3\\}\) b. \(\\{3,2,1\\}\) c. \(\\{0,1,2,3\\}\)
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