1. Let A = {1,3,5}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule     (X,Y) ∈ R ⇔ (X ∩ Y = Ø) ∧ (X ∪ Y = A). (a) Prove or find a counterexample for the following properties and based on the findings from the properties, conclude whether R is a graph, partially ordered set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the relation R.: antisymmetry asymmetry symmetry irreflexivity reflexivity transitivity uniqueness

Q: 1. Consider the relation R = {(a, a),(b, b), (c, c), (d, d),(a, b), (b, a)} on set A = {a,b,c,d}. Is…

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Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: Answer the following question accordingly:

A: Given set is  B={1,2,3,4}

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: Let S ⊆ N be the set that contains exactly all prime numbers greater than 4 and let R ⊆ S x S be the…

A: Let  be the set that contains exactly all prime numbers greater than .Let be a relation defined by…

Q: 7. Let S = {1,2,3, ...,8}. Let R be the relation on S defined by the following: %3D xRy + xy is a…

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Q: 2) Define a relation R from {a, b, c} to {u, v} as follows: R = {(a, v),(b, u),(b, v),(c, u)}. a)…

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Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: 3. Show that the relation R (called lexicographic ordering) defined on Z x Z by: (a, b)R(c, d) if (a…

A: The lexicographic ordering relation R on ℤ×ℤ is defined by, a, bRc, d if a>c or a=c and b≥d Show…

Q: 1. Let A = {1,2,3,4,5}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule     (X,Y)…

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Q: Let A = {2,4,6}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule     (X,Y) ∈ R ⇔…

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Q: 1. Let A = {1,3,5,7}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule     (X,Y) ∈…

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Q: Select the correct statement(s) for the relation R, defined on the set A = { a, b, c, d, e } by R=…

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Q: Let I be the set of all straight lines in the plane. Define and equivalence relation R by x R y iff…

A: Let, R be a relation on L(set of all straight lines in the plane) defined as, xRy iff x and y are…

Q: . Let A = {1,2,3,4}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule     (X,Y) ∈ R…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

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Q: Please answer the part (B). I have got a solution for the question on this platform but the answer…

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Q: 3. Let X be a set and S and R equivalence relations on X. Prove or give a concrete counter example…

A: Since you have asked multiple questions, we will solve the first and second question for you. If you…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 6. A small metal bar, whose initial temperature was 20°C, is…

A: Given,Initial temperature is .Then,Then, by the formula of of Newton's law of heating we…