Questron 5. Check whether the relation R in R defined by R = {(a, b): a < b³} is reflexive, symmetric or transitive.

Q: Let R be a relation that is symmetric and antisymmetric. Show that R is transitive

A: Let R be the relation which is symmetric and Anti-symmetric.We will show that R is transitive, that…

Q: i Determine whether or not the relation R on the set of all real numbers is reflexive, symmetric,…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. Is R reflexive?…

A: Given:  R is a relation defined on P 1, 2, … , 100 by A R B  if and only if A ∪ B is even. We have…

Q: Let R be the relation defined on P({1, . . . , 100}) by A R B    if and only if |A ∪ B| is even.…

A: Relation on a set

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: The given relation is not an equivalence relation. First check if the relation R is reflexive.…

Q: 1. Show that which of these relations on the set of all functions on Z→Z are equivalence relations?…

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Q: Let A={5,6,7,8,9,10} and define a relation S on A as follows xSy 2|(x-y) (a) Is 5S6? Why?

A: Consider the provided question,

Q: Consider the following relation R on R: (2, y) € R if and only if Va - y E Q. What are the…

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Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: Reflexivity: Since x≠x+2 , therefore, (x,x)∉R and hence R is not reflexive.   Symmetricity: Let…

Q: Let - be the relation on R\{0} given by x ~ y if and only if xy is positive. Prove that this is an…

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Q: Let R be the relation defined by x R y =x<y° Determine if R is an order relation on N? on Z? Justify…

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Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: If a relation R on a set A is antisymmetric, then R is not symmetric.

A: To determine whether the given statement is true or false.

Q: b. Define a relation SER XR by S ={ (x,y) E R × R |x – y € Z }. Prove that S is an equivalence…

A: By equivalence relation, we mean that the relation is reflexive, symmetric, and transitive.Here we…

Q: 8. Define a relation R on the set J = {0, 1,3,4,5,6} as follows: For all x, y EJ, x Ry ⇒ 4x² + y².…

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Q: 11. Prove or disprove: if a relation R is transitive, then R-1 is transitive.

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Q: Define a relation C from R to R as follows: For any(x, y) ∈ R × R, (x, y) ∈ means that x2 + y2 = 4…

A: Topic = function

Q: Let R be the relation defined by x R y x² < y² Determine if R is an order relation on N? on Z?…

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Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

A: Solution:

Q: 3. Let R be the relation defined on P({1,..., 100}) by ARB if and only if |AU B| is even. Is R…

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Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

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Q: Question 5: Check whether the relation R in R defined as R = {[a, b): as b} is reflexive, symmetric…

A: Introduction :--

Q: Let R be the relation on Z defined by    R = {(a,b): a, b ∈ Z, a – b is an integer}.Find the domain…

A: R = {(a,b): a, b ∈ Z, a – b is an integer}. We know that the difference of two integers is always an…

Q: Let R be a relation on Z. Then Ris an equivalence relation if it is defined by xRy if and only if…

A: R is an equivalent relation iff R is reflexive. R is symmetric. R is transitive.

Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y ∈…

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Q: Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or…

A: The given relation R is defined as follows.

Q: A relation R defined on the set of real numbers is such that x R yand y Rx >x = y. R is said to be…

A: Properties  used :- (i) a R a  for all a∈ A, [Reflexivity] (ii) a R b  and  b R a ⇒ a = b,…

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: 2. Consider the relation on the natural numbers N defined as follows: for all x, y e N, xRy if and…

A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

Q: Define a relation R on Z by xRy → x = y + 5k for k E Z. Prove that R is an equivalence relation by…

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Q: Let R be the relation on N defined by x R y if x and y share a common factor other than 1. Determine…

A: The relation R is defined as xRy on natural numbers Nsuch that x and y share a common factor other…

Q: B Let A = {(x,y) |x-yeQ for x, y = R} be a relation on K. Which statement best describes problem?…

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Q: t R be the relation on the set of ordered pairs of positive integers ch that ((a,b), (c,d)) e R if…

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Q: Show that the relation R in the set {1,2,3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is…

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Q: Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

A:

Q: Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} issymmetric but neither…

A: Given, relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)}.

Q: Provide a rule to define a relation R on N that is reflexive and transitive but not symmetric. Prove…

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Q: RUR and RNR symmetric relations on X. are Show that R=Z xZ is an equivalence relation.

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Q: Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive andtransitive but not…

A: Given, the relation R in R defined as R = {(a, b) : a ≤ b}.

Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

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Q: Suppose you have the following relation: R: A-A where A = (a, b, c, d, e) %3D R= ( (a, b), (a, e),…

A: Given relation is R:A-&gt;A where A={a,b,c,d,e}R={(a,b)  , (a,e) , (b,e) }determine whether it is…

Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: LeA R be the relation defined the se4 Nx Z that (xy)EIC on so if and only if a) What is. the domain…

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Q: Let a relation R on R2 be given by (x,y)R(x’,y’) provided that x-x’ and y-y’ are integers. Prove…

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Q: b) Let S = { (x, y) | x, y E R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

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Q: Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2),…

A: To find the transitive closure of a relation, we just add the ordered pairs that completes the…

Q: i Determine whether or not the relation R on the set of all real numbers is reflexiv netric,…

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Q: Let R be a relation and S its reverse. Show that R is injective if and only if S is well defined,…

A: Consider the provided question, Given that, R be a relation and S its reverse. Let R is a relation…