Let R be the relation defined on Z by aRb it a+b is even Find the number of distinct classes? Select one: O a.2 V O b. O a. None of them O c.3 O e. 4

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: 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 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: Let A = { 3, 9}, R relation on A defined R by. R = {(a, b): a +b = 12 ,a, b E A }. Write R. O a. {…

A: Given that A={3,9} R is a relation on A defined by R={(a,b):a+b=12,a,b belongs to A}

Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: Q 6 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,…

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Q: Let A={1,2,3} and B={-2,-1,0}. Define a relation R from S to T as follows: For all (x,y) in AxB,…

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Q: Let A be the set of all strings of 0's, l's, and 2's of length 4. Define a relation R on A as…

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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 A = {n| 3 < n S 30} and define a relation on A such that aRb iff a |b. List the relation set R.…

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

A: Solution : Given :             A = {3, 5, 7, 8} ,                         S is a relation from A to…

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: 2. The following relations are on {1,3,5}. Let r be the relation æry iff y = a + 2 and s the…

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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 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 S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b}.…

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Q: Let Y = {0, 1,2} and Z = {0, 1} and define a relation R from A to B as follows: Given any {x,…

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Q: Let X = {a, b, c}. Define a relation J on P(X) as follows: For all sets A and B in P(X), AJB A ANB #…

A: a) No  b) Yes  c) Yes

Q: 11. Let C= (0, 1, 2) and D= (2,4, 6, 8) and define a relation R from A to B as follows: For all (x,…

A: We have to determine the above terms for the given relation.

Q: 3. Define a relation S from R to R as follows: For all (x, y) e R xR, (x, y) eS means that x2 y. a.…

A: Given x,y∈S  Mean x≥y    x,y∈R×R

Q: 5. Define a relation Sfrom R to R as follows: For all (x, y) ERXR, (x, y) E S means that x 2y. a. Is…

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Q: Let R be a partial order relation on Z*. For any positive integers a and b, (a, b) E R if a|b. Are…

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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 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: Part II: Prove/Disprove the following 2. Let R be the relation on Z, defined as follows: Vm, n e Z,…

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Q: Define a relation S from R to R as follows:…

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Q: 1. Let A = (2, 3, 4} and B = {6, 8, 10) and define a relation R from A to B as follows: For all (x,…

A: Relation

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

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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: b) For a set X = {1, 2, 3, 4}, let P be the partition {{1,3}, {2, 4}}. The partition P induces a…

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Q: Let R be an equilene relation defineed an IN as follows ! 2-8(x)ENIN Y-y alivisible by3}

A: It is given that let r be an equivalence relation defined an 1n as follows R={(x,y) belongs to N*1N…

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: 2. Let A={1, 2, 3, 4, 5, 6} and let R be a relation on A defined as follows: Va,be A, (a,b)…

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

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Q: 3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether…

A: Reflexive: (x,y) R (x,y) As x+y=x+y Symmetric : if (a,b)R(c,d) then a+b=c+d. Since c+d=a+b then…

Q: Let A={1,2,3} and B={-2,-1,0}. Define a relation R from S to T as follows: For all (x,y) in AxB,…

A: We will find out the required values.

Q: Let Z be the set of all integers and R a relation on Z defined R= {(x,y) E Z × Zx = y +1}.Which of…

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Q: Let E =(1, 2, 3} and F = {-2, -1, 0} and define a relation T from E to F as follows: For all (x, y)…

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Q: 6. Define a relation from R to R as follows: For all (x, y) ER X R, (x, y) ER means that y = x2. a.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Let R be the relation on S={1,2,3} given by R={(1,1).(1,2).(2.1).(2.2),(3,1).(3.2)}. Then the…

A: Answer is mentioned below

Q: 10) Let R be a relation on A = {1,2,3,4,5,6,7} as x R y x+y 6. a. Find relative set R(B), where B =…

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Q: The relation on the set of integers R= {(x,y):5 divides x +y} is O a. none of the choices O b.…

A: Use the relevant definitions.

Q: (4) Let A={0,1,2}. R is a relation defined on A as: V x.y E A, xRy 2|(x-y). Represent R using set…

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Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

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

A: a) R be the relation on ℤ defined as follows:       a,b∈ℤ, a~b if and only if 'a' is a multiple of…

Q: 2. Let C = D = {-3, –2, –1, 1, 2, 3} and define a relation S from C to D as follows: For all (x, y)…

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Q: Let R be a relation on the set A = {1,2,3,4,5, 6} defined by R = {(a,b) E A x A| a + b < 9}. a. List…

A: A ={1,2,3,4,5,6}

Q: Define a relation R on Z as follows: For all integers m and n, m Rn = 5|(m² - n²). (a) Is 1 R (-4)?…

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Q: Let S = {(x,y) : x, y € R} = R². Define an equivalence relation on S (i.e. a subset of S × S = R² ×…

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