| № |
Condition |
free/or 0.5$ |
| m97689 | Write the dual statement for each of the following set- theoretic results.
(a)
(b) A = A ∩ (A U B)
(c)
(d) A = (A U B) ∩ (A U θ) |
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| m97695 | Write the following argument in symbolic form. Then either verify the validity of the argument or explain why it is invalid. [Assume here that the universe comprises all adults (18 or over) who are presently residing in the city of Las Cruces (in New Mexico). Two of these individuals are Roxe and Imogene.]
All credit union employees must know COBOL. All credit union employees who write loan applications must know Excel.1 Roxe works for the credit union, but she doesn t know Excel. Imogene knows Excel but doesn t know COBOL. Therefore Roxe doesn t write loan applications and Imogene doesn t work for the credit union. |
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| m97699 | Write the negation of each of the following statements as an English sentence - without symbolic notation. (Here the universe consists of all the students at the university where Professor Lenhart teaches.)
(a) Every student in Professor Lenhart s C++ class is majoring in computer science or mathematics.
(b) At least one student in Professor Lenhart s C++ class is a history major. |
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| m97700 | Write the negation of each of the following true statements. For parts (a) and (b) the universe consists of all integers; for parts (c) and (d) the universe comprises all real numbers.
(a) For all integers n, if n is not (exactly) divisible by 2, then n is odd.
(b) If k, m, n are any integers where k - m and m - n are odd, then k - n is even.
(c) If x is a real number where x2 > 16, then x < - 4 or x > 4.
(d) For all real numbers x, if | x - 3| < 7, then - 4 < x < 10. |
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| m97701 | Write the next three rows for the Pascal triangle shown in Fig. 3.4 |
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| m97757 | Zelma is having a luncheon for herself and nine of the women in her tennis league. On the morning of the luncheon she places name cards at the ten places at her table and then leaves to run a last-minute errand. Her husband, Herbert, comes home from his morning tennis match and unfortunately leaves the back door open. A gust of wind scatters the ten name cards. In how many ways can Herbert replace the ten cards at the places at the table so that exactly four of the ten women will be seated where Zelma had wanted them? In how many ways will at least four of them be seated where they were supposed to be? |
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| m97786 | Third·Order Verification Verify that the vector functions . , and of Example 8 are indeed solutions of system (8), and that they are linearly independent. |
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| m97787 | Third·Order Verification Verify that the vector functions . , and of Example 8 are indeed solutions of system (8), and that they are linearly independent. |
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| m97788 | Third·Order Verification Verify that the vector functions . , and of Example 8 are indeed solutions of system (8), and that they are linearly independent. |
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| m97789 | Solve the second order coupled system of ordinary differential equations by converting it into a first order system involving four variables. |
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| m97790 | Solve the second order coupled system of ordinary differential equations by converting it into a first order system involving four variables. |
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| m97791 | Let be the sample space for an experiment with events A, B ⊂ . If Pr(A|P) = Pr(A ∆ B) = 0.5 and Pr(A U B) = 0.7, determine Pr(A) and Pr(B). |
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