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. (i) Determine whether the relation R is a partial order on the set A. Justify your answer. Draw the Hasse diagram of the relation R on A, or explain why the Hasse diagram does not exist. (ii)

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A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

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Q: Find, for each part of the question, an example of a set S and two relations R1 C S x S and R2 C S x…

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Q: Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y e A , x R y = 3…

A: Given A = {2,3,4,6,7,9} xRy ⇔ 3 divides (x-y) Therefore 1)  R = (2,2) , (3,3) , (4,4) , (6,6) ,…

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Q: 5. Determine whether the following relation is i) an equivalence relation ii) a partial ordering. R=…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

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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 if and…

A: Given that:                      A={2,3,4}B={8,9,10}H is an relation from A to B such that: (x, y)∈H…

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A: Solution:

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Q: S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and…

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Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A| < [B|…

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Q: Define the relation R on Z as follows: for x, y ∈ Z, xRy if and only y−x ≥ 0. Determine whether R is…

A: partial order means reflexive and antisymmetric.

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Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: We have: The relation is: R=a,c,b,a,c,d,d,b

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

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}

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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: b) 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 |…

A: The given set is  A= { 2,4,6,12,16,18,24,32} Required to prove : the given relation is a partial…

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A: If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

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Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A]< |B|…

A: Given T be the partial order relation on P1,2,...,20 defined by ATB if and only if A&lt;B or A=B.

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A: As per the condition, in every order pair there should be only 1 letter in common.

Q: 1. Let A = {cat,dog,bird,rat} and R be a relation on A defined by {(x,y) : x and y have at least one…

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Q: Let R be a relation on A = {5, 6, 8, 9} and R {(8,8), (5,5), (6, 8), (5, 9), (9, 9), (9,5), (6, 6)}.…

A: Given that  R=(8, 8), (5, 5), (6, 8), (5, 9), (9, 9), (9, 5), (6, 6)

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: Let R be a relation on A = {1, 2, 6, 7} and R = {(6,6), (2,2), (7, 1), (1, 1), (7,7), (1,7)}. Are…

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Q: Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A…

A: Given, A=1,2,3 We can write the above set as, 1,2,3×1,2,3=1,1,,1,2,1,3,2,1,2,2,2,3,3,1,3,2,3,3

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Q: 1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check…

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Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is 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: 1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x²…

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