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Chapter 3: Problem 1
Which of the following sets are equal? a) \(\\{1,2,3\\}\) b) \(\\{3,2,1,3\\}\) c) \(\\{3,1,2,3\\}\) d) \(\\{1,2,2,3\\}\)
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Professor Diane gave her chemistry class a test consisting of three questions. There are 21 students in her dass, and every student answered at least one question. Five students did not answer the first question, seven failed to answer the second question, and six did not answer the third question. If nine students answered all three questions, how many answered exactly one question?
For a universe \(\mathscr{U}\) and sets \(A, B \subseteq \mathscr{q}\), prove each of the following: a) \(A \triangle B=B \triangle A\) b) \(A \Delta \bar{A}=9 L\) c) \(A \Delta \varphi_{L}=\bar{A}\) d) \(A \Delta \emptyset=A\), so \(\emptyset\) is the identity for \(\Delta\), as well as for \(U\)
At a high-school science fair, 34 students received awards for scientific projects. Fourteen awards were given for projects in biology, 13 in chemistry, and 21 in physics. If three students received awards in all three subject areas, how many received awards for exactly (a) one subject area? (b) two subject areas?
Determine which of the following statements are true and which are false. a) \(\mathbf{Z}^{+} \subseteq \mathbf{Q}^{+}\) b) \(\mathbf{Z}^{*} \subseteq \mathbf{Q}\) c) \(\mathbf{Q}^{+} \subseteq \mathbf{R}\) d) \(\mathbf{R}^{*} \subseteq \mathbf{Q}\) e) \(Q^{*} \cap R^{*}=Q^{*}\) f) \(\mathbf{Z}^{*} \cup \mathbf{R}^{*}=\mathbf{R}^{*}\) g) \(\mathbf{R}^{*} \cap \mathbf{C}=\mathbf{R}^{*}\) b) \(\mathbf{C} \cup \mathbf{R}=\mathbf{R}\) D) \(Q^{*} \cap \mathrm{Z}=\mathrm{Z}\) j) \(\mathbf{Z} \cup \mathbf{Q}=\mathbf{Z}\)
Darci rolls a die three times. What is the probability that a) her second and third rolls are both larger than her first roll? b) the result of her second roll is greater than that of her first roll and the result of her third roll is greater than the second?
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