Problem 6. Let ? = {?, ?, ?, ?}. Define ? on ? as follows: ? = {(?, ?), (?, ?), (?, ?), (?, ?), (?, ?)} (a) Find the reflexive closure of R.
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Problem 6. Let ? = {?, ?, ?, ?}. Define ? on ? as follows: ? = {(?, ?), (?, ?), (?, ?), (?, ?), (?, ?)}
(a) Find the reflexive closure of R.
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- Problem 1: A. In the piggy bank I have 90 coins. 20 quarters, some pennies, and 30 half dollars. How many different ways can these coins be put into a row? B. Find all possibilites of a relation on {4, 5, 6} that is reflexive and transitive, but not symmetric. Discrete MathBecause of what theorem?Question 17 With regard to composition of relations, If S and R are both anti-reflexive, then s∘r is anti-reflexive. True False
- What is the correct answer to "Find St, the transitive closure of S."? Original Problem Statement in image.I need help with this discrete mathematics problem involving proving linear orderingA designer is creating various open-top boxes by cutting four equally-sized squares from the corners of a standard sheet of 8.5 inches by 11-inch paper, and then folding up and securing the resulting 'flaps' to be the sides of the box. Let x represent the varying side length of the square cutouts in inches. Let l,w, and h represent the varying length, width, and height of the box (in inches), respectively. Note that the width and length dimensions are such that w<l. Let V represent the varying volume of the box in cubic inches.
- Derive the following problems in the attachment.Problem 2Let A be a set, and let R be a relation on A. Suppose that R is symmetric and transitive.Find the flaw in the following alleged proof that this relation is necessarily reflexive. “Letx ∈A. Choose y ∈A such that xRy. By symmetry know that yRx, and then by transitivitywe see that xRx. Hence R is reflexive.”Problem 4Let A be a set, and let R be a relation on A.1. Suppose R is reflexive. Prove that ∪x∈A[x] = A.2. Suppose R is symmetric. Prove that x ∈[y] if and only if y ∈[x], for all x, y ∈A.3. Suppose R is transitive. Prove that if xRy, then [y] ⊆[x] for all x, y ∈A.
- I have a question on part (f) and (g) on this problemRelated to the solution for exercise problem 12, in section 7.4 of textbook "Discrete Mathematics: Introduction to Mathematical Reasoning, 4th Edition": What is the process for how the function "f(x) = (b - a)x + a" was assumed given the following information: S denotes the set of real numbers strictly between 0 and 1. That is, S = {x ∈ R | 0 < x < 1}. Let a and b be real numbers with a < b, and suppose thatW = {x ∈ R| a < x < b}. Prove that S and W have the same cardinality. I understood the later steps of proving the function being one-to-one and onto, but not sure how the function f(x) came to be in the first place.I need help with this discrete mathematics problem involving disjointedness