Problem 5. State which of the following sets are finite and which are infinite: (1) A = {x : x e Z and x - 4x + 3 = 0} (i) B = {x : x e Z and x is even} (iii) C = {x : x e Z and x2 = 49} (iv) D = {x : x € Z and x > - 9}
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- I am taking a Topology course and was wondering if you could help me with Problem 2 and 3 of the worksheet that is attached.Question: 1 In the following problems ((a) - (e)), your task is to write down each of the following sets by listing its members. (a)The set of all possible outcomes of tossing a coin three times. Call this set U in the following problems in question 1. (b) {x ∈ U | x has more heads than tails} Call this set E. (c) {x ∈ U | x has at most two heads or at most two tails} Call this set F. (d) (E ∪ F) (e) (E ∩ F) In the following problems ((f) - (j)) you are given the description of a set. Your task is to write down the set in the formal language of set theory by specifying the membership condition of the set. There are many possible answers here, but make sure that the condition you specify actually determines which elements belong to that set. (f) The set of natural numbers N strictly less than 6 (g) The set of integers Z whose square is less than 17 (h) Assume the numbers in this set are natural numbers N. {0, 10, 20, 30, 40, 50, . . . } (i) Ecin U (j) The intersection of…question 2 Hiring workers A company payshis skilled workers S15 per hour in his departmentassembly tool. semi-skilled workersin that department they earn S9 per hour To the employeestwo of shipments are paid SIO per hour Because of aincrease in orders, the company needs to contractemploy a total of 70 workers in the departments ofassembly and shipping Will pay a total of $760 per hourto these employees. Because of a contract with the unionlaw, twice as many semi-semi-workers should be employed.lified than skilled workers. How manysemi-skilled workers, skilled workers and employees ofshipments should hire the company? Note: Solve by Inverse-Excel # OF SEMI-SKILLED WORKERS # OF SKILLED WORKERS # OF SHIPPING WORKERS
- 37-If we substitute the corners of closed polygon values in objective function, the value of Z at points R,0,U,W are 12,0,17,19,16 respectively. The variables at these points are (2.5,0), (0,0), (1.5,2.5), ( 3.2, 2.1), and (2.1, 1.2) respectively. Based on the given data, which one of the product mix the company can choose? O a. 3.2 units of product X and 2.1 units of product Y O b. 2.5 units of product X and 0 units of product Y O c. 1.5 units of product X and 2.5 units of product Y O d. 2.1 units of product X and 1.2 units of product YProblem 3The power set of any set A is denoted by P (A) and is defined as the set of all subsets ofA, including the empty set and the set A itself. Think of ⊆ as defining a relation on P (A)where P, Q ∈ P (A) are related if and only if P ⊆ Q. Is this relation reflexive, symmetric,and/or transitive?