Let {2,3,4}{2,3,4} and {8,9,10}{8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and only if y−x/2 is an integer.  Find the number of elements of H

Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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Q: let A={1,2} and B={1,2,3} and define a relation R from A to B as follows: given any (x,y)E AxB…

A: Given: A=1,2 and B=1,2,3 and R:A→B such that x,y∈R⇒x-y2 is an integer. To find: A×B  and R…

Q: Which of the following relations on the set A = {0, 1, 2, 3} is an equivalence relation? Check all…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Let A={3,4,6,7}, and define a relation R on A as follows: For every x, y belong to A, xR y x|y.…

A: We first write elements of R then we form diagraph and then we write the corresponding adjacency…

Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: Let P = {2,3,4,5} and define a relation R from P to P as follows: For all (x,y)∈P×P,(x,y)∈R if and…

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Q: {0, 1, 2, 3, 4, ...} and define the relation - on A by: x~y if x – y is divisible by 3 Determine…

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Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let A = {2, 4, 6, 12, 16, 18, 24, 32} and R be the relation on A where x R y if and only if x | y.…

A: A= 2,4,6,12,16,18,24,32 R is define as xRy if x/y  so, R = (2,2) (2,4), (2,6) (2,12) , (2,16) (2,18)…

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

A: We will find out the required values.

Q: Let R be a relation on Z defined by (x,y)ER if and only if 5(x-y)=0. Formall state what it means for…

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Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

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Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y^x, y = A} R"X =…

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Q: Let {2,3,4}{2,3,4} and {8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and only if…

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Q: Let S ⊆ N, and for any c, d ∈ N, consider a relation R such that cRd if and only if there exists a ∈…

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: Let A = {1, 2, 3, 5, 6, 10, 15, 30} and R be a relation on A such that aRb if and only if a is a…

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Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: %3D For all (x, y) E A × A, (x,…

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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: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all (x, y) ∈ A…

A: A=3,4,5B=1,2,3,4R=x,y: x∈A, y∈B ∋xy&gt;7 a. R=3,3, 3,4, 3,5, 4,2, 4,3, 4,5, 5,2, 5,3, 5,4, 5,5

Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: Let R be a relation on a set A. Define a relation ∼ on A as follows: for every a, b ∈ A, a ∼ b if…

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Q: Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: 14. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Given sets  A={9,11,12,14} and  B={1,2,3,4}  The relation R from A to B is defined by ,…

Q: Let R1 be the relation on Z+ such that ¤R¡y if and only if ry > 3. (Recall that Z+ = {1,2, 3, 4,…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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Q: Let {2,3,4} {2,3,4} and {8,9,10} {8,9,10}. Define a relation H from A to B such that (x,y)∈H(x,y)∈H…

A: Given A={2,3,4} B={8,9,10}

Q: Let G = {-2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every (x,…

A: Given,            G=-2, 0, 2  and   H=4, 6, 8and  define a relation v from G to H as follows.For…

Q: Let A={1, 2, 5, 10}. Define the relation R on the base set A by: xRy if x/y is a whole number. Then…

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Q: (3) Let A={1,3,5,7}, B={0,4,8}. Define the relation R as: For all x E A and y E B, xRy , if and only…

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Q: Let G = { -2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows: For all (x, y)…

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Q: 10 Let A={4,5,6,7,8,9,10,11,12,13} and define a relation S on A as follows xS y → 4|(x-y) (a) Is…

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Q: Let A = {1, 2, 3, 4} and R be a relation defined on A. Given that R= {(1, 1), (1, 3), (2, 2), (2,…

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Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

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Q: Let X be the set of all nonempty subsets of {1,2,3}. Then                X=…

A: Given,  X=1,2,3,1,2,1,3,2,3,1,2,3 R is defined as: For every A,B in X, ARB⇔the least element of A…

Q: Let A = {-5, -4, −2, 0, 3, 6, 8), and define an equivalence relation R on A as follows: (x, y) E R…

A: Let A = {-5, -4, -2, 0, 3, 6, 8}, and define an equivalence relation R on A as follows: (x, y) in  R…

Q: given the relation R define = (0,0), (0, 1), (0, 3), (1, 1), (1,0), (2, 3), (3, 3) on the set A = 0,…

A: Given that  R=0,0,0,1,0.3,1,1,1,0,2,3,3,3A=0,1,2,3 To draw the directed graph and determine whether…

Q: Define a relation R on the set J ={ 0, 1, 3, 4, ,5, 6 } as follows for all x, y E J x R y if and…

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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: Let A = Z. Define R to be the relation where a~b if ab > 0. Then R is equivalence relation.

A: We have given the set A = { Z : the set of integers }  R= { (a,b) : a,b belongs to Z and a.b &gt;0}…

Q: Let A= {2,3,4} B=  {6,8,10} Define relation R from A to B as follows;For all X,y

A: Given- A=2,3,4 and B=6,8,10 To Find- The relation R from A to B follows, for ∀∈x,y

Q: Consider the relation R on the set Z defined by a R b if and only if 3|(a+2b) for a, b ∈ Z. Show…

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Q: Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the…

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Q: let A= {a,b,c,d} and R= {(a,a),(a,c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. What is the…

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

A: A relation R between the elements of a set is said to be equivalence relation if it is: Reflexive…

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: 5. In the set A = {1, 2,3,4, 5 }, a relation R is defined by R= (x, y): x,y € A and x < y}. Then R…

A: For Transitive,(a,b)∈R(b,c)∈R(a,c)∈R

Q: 6. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Answer for sub question a: Given A=9,11,12,14, B=1,2,3,4. The relation R:A→B is defined as follows:…

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

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