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

Q: A relation R defined on the set of real numbers is such that xRy and yRx = x = y: R is said to be A…

A: There are many types of relations Symmetric Asymmetric Reflexive Transitive

Q: Is the relation R on X is reflexive, symmetric, weakly antisymmetric, antisymmetric, transitive?…

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Q: Let A = {x, y, z}. Write down a relation R on A that is not reflexive, not sym- metric, and not…

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Q: A relation Ris defined on N by a R b if a/b e N. For c, d e N, under what conditions is c R1 d?

A: An inverse relation is the set of ordered pairs obtained by interchanging the first and second…

Q: The relation R on X={1,2,3,4}defined by (x,y) € R if x=y.

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Q: Consider the following relation R on R: (x, y) ER if and only if y E Q. What are the properties of…

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Q: Let R be a relation from Q to Q defined by R = {(a,b): a,b ∈ Q and a – b ∈ Z}. Show that:(i) (a,a) ∈…

A: i) Given that a ∈ Q  a-a=0 ∈ Z So, (a,a) ∈ R for all a ∈ Q (proved)

Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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Q: Let R be the relation on N defined by R = {(n, m) EN x N: m=n+1). Then R is surjective. True False

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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: Consider a relation R on Z defined as follows: xRy → xy is even. a. Give a counterexample to show…

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Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…

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Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R symmetric? Is it…

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

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

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Q: Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric?

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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: In the Cartesian plane = {(x, y): x,y E R} consisting of points with rectangular coordinates (x, y),…

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Q: Let L be the set of all lines in a plane and R be the relation in L defined asR = {(L1, L2) : L1 is…

A: The given relation R is defined as follows.

Q: Let R be the relation on R defined by R= {(x, y) E R × R | x² + y² = 4 or x = y²}. Answer each of…

A: Given that R be the relation on ℝ defined by,R=x,y∈ℝ×ℝx2+y2=4 or x=y2

Q: T is a function?

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Q: Let R be a relation from A={−1,0,1,2} to B={a,n,i} such that (x,y) provided that x is non-negative…

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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: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

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

A: A relation R is said to be reflexive on a set A if for all a∈A, a,a∈R A relation R is said to be…

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

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

Q: Consider the relation S on N defined by uSy⟺5|(y+u). Is it reflexive?

A: No it is not a reflexive relation

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

A: (x,y) ∈ R × R (x,y) ∈ C means    x2 + y2 =4

Q: Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is…

A: Given, Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) :…

Q: A relation R is defined on Z by a R b if |a – b| < 2. Which of the properties reflexive, symmetric…

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Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: Let A be the set of all lines in the plane. Define a relation R on A as follows. For every /, and /,…

A: Let A be the set of all lines in the plane . Define a relation R on A as follows For every l1 and l2…

Q: Let R be the relation on the set of real numbers such that x R y if and only if x and y are real…

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Q: Prove A = BH (x)A = (Vx)B without using the equivalence theorem.

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (r, y)R(z, w)…

A: We will prove the given statement.

Q: Let R = {(f, g) | f(1) = g(1)} be a relation defined on the set of func- tions from Z to Z. Is R an…

A: Let R be a relation on a set A. Then R is said to be an equivalence relation if it is reflexive,…

Q: Let S be the following relation on ℂ: S = {(x, y) ∈ ℂ2 : y − x is real}. Prove that S is an…

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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: Let ℝ denote the set of real numbers, and  β:={(x,y)∈ℝxℝ| xy≥∅} be a relation on ℝ. Which…

A: The given relation β⊂ℝ2 is: β=x,y∈ℝ×ℝ | xy≥0 The properties of a relation is: Reflexive Irreflexive…

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (2, w) in A, (r, y)R(z, w)…

A: Given that: A=Z+xZ+. Relation is:        For all (x, y) and (z, w) in A, (x, y)R(z, w)⇔x+w=z+y…

Q: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

Q: The relation xy >= 1 where x,y are on the set of all integers is reflexive. True False

A: Given relation xy≥1, where x,y are on the set of all integers

Q: Suppose there are two transitive relations R, S Disprove the claim that the composed relation S R…

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Q: Let - be a relation on N defined as: a ~b if a < (b – 1). (i) Is ~ reflexive? Prove your answer.…

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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 N defined by a R b if either a | 2b or b | 2a. Is R an equivalence…

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

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Q: (a) Let R be the relation on Z defined as follows: For a, b e Z, a~b if and only if a is a multiple…

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Q: Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

A: Given : 1,2, 2,9, 5,6