. Let S = P({1,2,3,4,5}.. Define equivalence class of the set {1,2,3}. equivalence relation ~ by X~Y iff X^{1,3,5}=Y^{1,3,5}. Give the an

Q: With a binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Show that R has the same cardinality as the interval (–2, 2) by building a bijection between the two…

A: This is a problem of Real Analysis and Topology.

Q: Thoorem: is not closed set

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Q: 1. For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it…

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Q: Give an example of a set in R ^ 2 with the usual topology that is not connected but has a connected…

A: Let's examine the  problem for path-connectedness example of a set in R2 with the usual topology…

Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: Define relations S and R on the set A = {x, y, z, w} as follows S = {(y, x), (x, w), (w, z), (x,…

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Q: that the boundary of a closed set is nowhere dense in

A: Matric space

Q: Let à = (-5, 4, Find the projection proja b =< 4) and b = (-4, 0, -1). of b onto a. -

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Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: Find the transitive closure of R={(0,1),(0,2),(1,1), (1,3),(2,2),(3,0)}

A: Given relation is                              R=(0, 1), (0, 2), (1, 1), (1, 3), (2, 2), (3, 0) we…

Q: the sets  [0,1] and  [0,1/2)∪(1/2,1] have the same cardinality, give an explicit bijection to show…

A: We will define a bijection from the set J  = [ 0 , 12 ) ∪(12 , 1]   to the set I =0 ,1   First we…

Q: 26. Use Algorithm 1 to find the transitive closures of these relations on {a, b, c, d, e}. a) {(a,…

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Q: The congruence modulo 5 relation is an equivalence relation on the set {0, 1, 2, 3, 4, 5, 6, 7,8,9,…

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Q: Let A={ 1, 2, 3, 4, 5} R={ (1,1), (1,2), (2,1), (2,2), (3,3), (3,4), (4,3), (4,4), (5,5) } Write the…

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Q: Let A = {a, b, c, d, e, f,g, h}, and let G and H be the following equivalence relations in A: %3D G…

A: Given that A = a , b , c , d , e , f , g , h . Also,  G and H are the following equivalence…

Q: The equivalence class of -2 for the relation congruence modulo 5 is о (... -11, -6, —1,4, 9, 14,…

A: Second option is correct.

Q: Let S = { (0,0), (0,3), (1,0), (1,2), (2,0), (3,2) } Find S', the transitive closure of S

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Q: Prove that (2,5) is an open set

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Q: Compute: Limit points. Interior of the set. Closure of the set. Boundary of the set of the set…

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Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: The relation by a = b (modn) is Partial Order Relation Ture O False O

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Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

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Q: 2. From the set of relation {(1,1), (1,2), (1,4), (2,1), (2,2), (2,4), (3,3), (4,3), (4,4)}, draw…

A: As per our guideline we are allowed to answer only one question. Kindly submit the other question as…

Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: 2. Determine the partition of B = {1,2,3,4,5,6,7,8,9,10} induced by the equivalence relation B…

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Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

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Q: The equivalence class of -1 for the relation congruence modulo 5 is о (.., -12, —7, —2,3, 8, 13, ..}…

A: The equivalence class of -1 is denoted as -1 and defined as -1=x mod 5; where x∈R. For example: take…

Q: denotes the set of subsp

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Q: Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the…

A: To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Q: The equivalence class of -1 for the relation congruence modulo 5 is O {...,-12, –7, –2, 3,8, 13,…

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Q: If {{1, 3, 5}, {2, 4}} is a partition of the set A = {1, 2, 3, 4, 5}, determine the corresponding…

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Q: Prove that derived set of a bounded set is also bounded.

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Q: For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set…

A: We have to solve given problem:

Q: Let S = {1,2,3, 4}. For each of the following relations on S give its transitive closure. a) {(1,1),…

A: Concept: In mathematics, the transitive closure of a binary relation R on set X is the smallest…

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

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Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Let A={1,2,3,4,5} and…

A: Let A=1,2,3,4,5 and R=1,1,1,3,1,4,1,5, 2,2, 2,3, 2,4, 2,5,  3,3, 3,4, 3,5, 4,4,  5,5 (a) The…

Q: There are 6 towns {A, B, C, D, E, F} with the following one way street relation {(A, B), (A, C), (B,…

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Q: Give a set that is not closed under addition

A: In the question we have to give a set that is not closed under addition.

Q: Let S = {0, 1, 2, 4, 6}. Test the following relation whether it has equivalence relation on S. R =…

A: Given relation R = {(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (0, 2), (1, 2), (4, 6)} on  S =…

Q: What is the composite

A: Let A,B and C be three sets. Suppose that R is a relation from A to B, and S is a relation from B to…

Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

Q: Our universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example,  R(3,-2)…

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Q: In the set A = {1, 2, 3, 4} is defined a relation R by %3D R = {(1, 1), (1, 3), (3, 4), (4, 3)}.…

A: Given set is A = {1, 2, 3, 4}  with relation R = {(1, 1), (1, 3), (3, 4), (4, 3)}

Q: Let P={1.2,3,4,12,36} and the relation set R={(1,1)…

A: The objective is to show that (P,R) is a poser. Represent the relation using the diagraph and then…

Q: I. Draw the directed graph and list the set of ordered pair of R, of the following. 1. If…

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Q: uppose (X,≺) is a well-ordering. Then (X,≺) is not isomorphic to (pred(X,≺,x),≺) for any x ∈ X.

A: Set theory