A is a finite non-empty set. The domain for relation Ris the power set of A.(Recall...
Aisa finite non empty set. The domain for relation Ris the power set of A. (Recall that the power set of Ais the set of a subsets of A. For X A and Y C AX is related to Y it X and Y have the same cardinality (le, XI = |Y1). Select the description that accurately describes relation Anti-symmetric and Refletve Anti-symmetrk and Anti-refedve Symmetric and Reflexive Symmetric and Anti-reflextve
Let P(X) be the power set of a non-empty set X. For any two subsets A and B of X, define the relation A B on P(X) to mean that A union B = 0 (the empty set). Justify your answer to each of the following? Isreflexive? Explain. Issymmetric? Explain. Istransitive? Explain.
2. (24 pts) True/False. Circle T or F. No explanation needed. (a) T F If Ris the relation whose digraph is below, then Ris reflexive. (b) T F For the relation from part (a), R is symmetric (C) T F The relation Son {a,B,y,g} whose matrix is 100.1 - 0 1 0 0 0 0 1 0 1001 is an equivalence relation. (d) T F The relation S from part (C) is a partial order. (e) T F Let the...
Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of counting nuobors and the relation {(X Z〉 | Ye F and Z € Fand y-2). This relation is just a version of the usual subset relation, but restricted to only apply to the sets in F Prove: CFis a partial order. Prove: Cis not symmetric and connected. Prove: If R is an equivalence relation, it is also a euclidean...
probelms 9.1
9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
PROBLEM 5 The number of watermelons in a truck are all weighed on a scale. The scale rounds the weight of every watermelon to the nearest pound. The number of pounds read off the scale for each watermelon is called its measured weight. The domain for each of the following relations below is the set of watermelons on the truck. For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither Symmetric, anti-symmetric, or neither • Transitive or...
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if a) x + y = 0 b) x= ±y. c) x-y is a rational number. d) = 2y. e) xy ≥ 0. f) xy = 0. g) x=l. h) r=1 or y = 1
8. On the set A = {1,2,3,4,...,20}, an equivalence relation R is defined as follows: For all x, y € A, xRy 4(x - y). For each of the following, circle TRUE or FALSE. [4 points) a. TRUE or FALSE: There are only 4 distinct equivalence classes for this relation. b. TRUE or FALSE: If you remove all the even numbers from A, the relation would still be an equivalence relation. C. TRUE or FALSE: In this equivalence relation, 2R5...
b and c please explian thx
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post the question from the book
Let 2 be a non-empty set. Let Fo be the collection of all subsets such that either A or AC is finite. (a) Show that Fo is a field. Define for E e Fo the set function P by ¡f E is finite, 0, if E is finite 1, if Ec is finite. P(h-10, (b) If is countably infinite, show P is finitely additive but not-additive. (c)...
Recall that the power sert P(S) of a set S is the collection of all subsets of S. For A= {1, 2, 3} and B = {x, y} , calculate the following cardinalities: (Please show your work so I can follow along, Thanks!) 1. |P (A) | 2. |P (B) | 3. |A × B2 | 4. |P (A × B) | 5. |P (A) × B| 6. |P (P (A)) |