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.
Let P(X) be the power set of a non-empty set X. For any two subsets A...
A is a finite non-empty set. The domain for relation Ris the power set of A.(Recall that the power set of A is the set of all subsets of A. For X A and Y C A, X is related to Y it X is a proper subsets of Yle, X CY). Select the description that accurately describes relation R. Symmetric and Anti-reflexive Symmetric and Refledve Anti-symmetric and Anti-reflexive Anti-symmetric and Refledive
Let S be the set of all subsets of Z. Define a relation,∼, on S by “two subsets A and B of Z are equivalent,A∼B, if A⊆B.” Prove or disprove each of the following statements: (a)∼is reflexive(b)∼is symmetric(c)∼is transitive
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
9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc (a) R is symmetric but not reflexive. (b) R is transitive and symmetric but not reflexive (c) R is reflexive and transitive but not symmetric (d) None of the above 10. Let R be an equivalence relation on a nonempty and finite 9. Define R the binary relation on N x N to mean (a, b)R(c, d) iff b|d and alc...
Consider the empty set as a relation, R, on any non-empty set S. Prove or disprove: R is transitive.
2. Let S 11,2,3,4,5, 6, 7,8,91 and let T 12,4,6,8. Let R be the relation on P (S) detined by for all X, Y E P (s), (X, Y) E R if and only if IX-T] = IY-T]. (a) Prove that R is an equivalence relation. (b) How many equivalence classes are there? Explain. (c) How mauy elements of [ø], the equivalence class of ø, are there? Explain (d) How many elements of [f1,2,3, 4)], the equivalence class of (1,2,3,...
4. Let S be the set of continuous function f: [0;1) ! R. Let R be the relation defined on S by (f; g) 2 Rif(x) is O(g(x)). (a) Is R reflexive? (b) Is R antisymmetric? (c) is R symmetric? (d) is R transitive? Explain your answer in details. Use the definition of big-O to justify your answer if you think R has a certain property or give a counter example if you think R does not have a certain...
4·Let A and B be non-empty subsets of a space X. Prove that A U B is disconnected if A n B)U(A nB) 0. Prove that X is connected if and only if for every pair of non-empty subsets A and B of X such that X A U B we have (A B)U (An B)O.
b and c please explian thx i 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)...
1) Let R be the relation defined on N N as follows: (m, n)R(p, q) if and only if m - pis divisible by 3 and n - q is divisible by 5. For example, (2, 19)R(8,4). 1. Identify two elements of N X N which are related under R to (6, 45). II. Is R reflexive? Justify your answer. III. Is R symmetric? Justify your answer. IV. Is R transitive? Justify your answer. V.Is R an equivalence relation? Justify...