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Let A = {1, 2, 3). Consider the following relation on A: R= {(1, 1), (1,...
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by R= {(1,3), (2,3), (3, 4), (4,4),(4,5), (5,6), (5,7)} (1) (6 pts) Find Rk for all k = 2, 3, 4, 5,... (2) (3 pts) Find the transitive closure t(R) of R by Washall's algorithm and draw the directed graph of t(R).
QI. Let A-(-4-3-2-1,0,1,2,3,4]. R İs defined on A as follows: For all (m, n) E A, mRn㈠4](rn2_n2) Show that the relation R is an equivalence relation on the set A by drawing the graph of relation Find the distinct equivalence classes of R. Q2. Find examples of relations with the following properties a) Reflexive, but not symmetric and not transitive. b) Symmetric, but not reflexive and not transitive. c) Transitive, but not reflexive and not symmetric. d) Reflexive and symmetric,...
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...
Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined by: xMy – 31(x - y). (Note: Unless you are explaining “Why not,” explanations are not required.) a. Draw the directed graph of M. b. Is M reflexive? If not, why not? C. Is M symmetric? If not, why not? d. Is M antisymmetric? If not, why not? e. Is M transitive? If not, why not? f. Is M an equivalence relation, partial order...
4. [3 marks] Let R be a relation on a set A. Let A {1,2, 3, X, Y} and R = {(1, 1), (1,3), (2,1), (3, 1), (1, X), (X, Y)} (a) What is the reflexive closure of R? (b) What is the symmetric closure of R? (c) What is the transitive closure of R?
I would like help with problem 1 and 3 with great detail
1. Let A nEZ: n21 Write down the elements of A Write down the elements of P(A) Write down the elements of Map(A, A) Write down the elements of idA Write down the elements of f E Map(Map(A, A), A): f(idA) 1 ents of Uf E Map(Map(A, 4),A) 2. Let A-(n E N : n < 20). Show that the relation R = {(a, b) e A ×...
Let A = { 1, 2, 3, 4, 5 }. Give examples of a relation over AxA that has exactly 5 elements that satisfy each of the following properties: Reflexive: Irreflexive: Symmetric: Antisymmetric: Transitive:
Discrete Mathematics. Let A = {2,4,6,8,10}, and define a relation R on A as ∀x,y ∈ A,xRy ↔ 4|(x−y). (a) Show R is an equivalence relation. (b) Give R explicitly in terms of its elements. (c) Draw the directed graph of R. (d) List all the distinct equivalence classes of R.
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f is 0(g)" on F is: (a) (4pt) Write down the definition for "f is O(g)". (b) (4pt) Prove that the relation is reflexive (c) (6pt) Prove that the relation is not symmetric. (d) (6pt) Prove that the relation is transitive.
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f...