Q

QuestionMathematics

Which of the following sets are equal? A = {x | x^2 − 4x + 3 = 0}, C = {x | x ∈ N, x < 3}, E = {1, 2}, G = {3, 1}, B={x|x^2−3x+ 2 = 0}, D = {x|x∈N, x is odd, x<5}, F={1,2,1}, H={1,1,3}. Hint: for the quadratic Equations, get the values of x which shall be elements of set A and B.) 2. List the elements of the following sets if the universal set is U = {a, b, c, ..., y, z}. Furthermore, identify which of the sets, if any, are equal. A = {x |x is a vowel}, C = {x |x precedes f in the alphabet}, B = {x |x is a letter in the word “little”}, D = {x |x is a letter in the word “title”}. 3. Let A= {1,2,...,8,9}, B={2,4,6,8}, C={1,3,5,7,9}, D={3,4,5}, E={3,5}. Which of the these sets can equal a set X under each of the following conditions? (a) X and B are disjoint. (c) X⊆A but X ⊈ C. (b) X ⊆ D but X ⊈ B. (d) X⊆C but X ⊈ A. 4. Consider the universal set U = {1,2,3,...,8,9} and sets A={1,2,5,6}, B={2,5,7}, C={1,3,5,7,9}. Find: (a) A∩B and A∩C (b) A∪B and B∪C (d)A\BandA\C (f)(A∪C)\Band(B⊕C)\A (c)AC and CC (e) A⊕B and A⊕C 5. The formula A\B = A ∩ B C defines the difference operation in terms of the operations of intersection and complement. Find a formula that defines the union A ∪ B in terms of the operations of intersection and complement. 6. The Venn diagram in Fig. (a) shows sets A, B, C. Shade the following sets: (a) A\(B∪C); (b)AC∩(B∪C); (c)AC∩(C\B). ( Note you can draw different diagram for each answer to avoid shading overlapping and congestion.) 7. Write the dual of each equation: (a) A=(BC∩A)∪(A∩B) (b) (A∩B)∪(AC∩B)∪(A∩BC)∪(AC∩BC)=U 8. Use the laws in Table 1 - 1 to prove each set identity: (a) (A∩B)∪(A∩BC) = A (b) A∪B=(A∩BC)∪(AC∩B)∪(A∩B) Section Two 9. Determine which of the following sets are finite: (a) Lines parallel to the x axis. (c) Integers which are multiples of 5. (b) Letters in the English alphabet. (d) Animals living on the earth. 1 10. A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of three popular options, air-conditioning (A), radio (R), and power windows (W ), were already installed. The survey found: 15 had air-conditioning (A), 12 had radio (R), 11 had power windows (W), 5 had A and P , 9 had A and R, 3 had all three options. 4 had R and W, Find the number of cars that had:(a) only W; (b) only A; (c) only R; (d) R and W but not A; (e) A and R but not W; (f) only one of the options; (g) at least one option; (h) none of the options. 11. Find the power set P(A) of A={1,2,3,4,5}. 12. Given A = [{a,b},{c},{d,e,f}]. (a) List the elements of A. (b) Find n(A). (c) Find the power set of A. 13. Let S = {1, 2, ..., 8, 9}. Determine whether or not each of the following is a partition of S : (a) [{1,3,6},{2,8},{5,7,9}] (b) [{1,5,7},{2,4,8,9},{3,5,6}] (c) [{2,4,5,8},{1,9},{3,6,7}] (d) [{1,2,7},{3,5},{4,6,8,9},{3,5}]

what is 100 * 9

2+2

# Question 10 There have been three waves of increases in opioid deaths from overdose in U.S. history. In 1990, what was the role of the pharmaceutical industry in causing this first spike? The pharmaceutical industry started paying financial incentives to doctors. The pharmaceutical industry began mixing opioids with another new experimental drug that many people were found to be allergic to. The pharmaceutical industry engaged in misleading marketing, making opioids appear to be safe. The pharmaceutical industry lobbied to include the level of pain as a fifth vital sign in medical care.

Factor using the sum or difference of two cubes formula. a3−27