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 # Ø. (a) Is {a} J {c}? Yes No (b) Is {a, b} J {b, c}? O Yes O No (c) Is {a, b} J {a, b, c}? Yes O No

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 a relation S be defined on A = {0, 1, 2, 3} as follows. s= {(0,0), (0, 3), (1, 0). (1, 2). (2,…

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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 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: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

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Q: The relation R defined on a set A is antisymmetric if (a, b) ER = (b, a) E R for (A) Every (a, b) ER…

A: A relation R is said to be antisymmetric if (a,b)∈R and (b,a)∈R implies a=b

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 A = {x, y} and let S be the set of all strings over A. Define a relation C from S to S as…

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Q: Let f: X → Y and define x~y if f (x) = f (y). Show that - is an equivalence relation on X.

A: The objective is to show that ~ is an equivalence relation on X.

Q: B and let R = {(x, y) E A x A | g(x) = g(v)}. Suppose g: A Show that R is an equivalence relation on…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: Consider the relation R on Z defined by the rule that (a, b) E R if and only if a + 26 is even.…

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Q: A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x;…

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Q: Let R be a relation defined on P(Z) defined by (A, B) E R if and only if AN B + Ø. Prove or disprove…

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Q: In this exercise, you want to show that a relation R C A? is transitive + R" C R for all n E N =…

A: In this problem, we have to show that a relation R ⊆ A2 is transitive if and only if Rn ⊆ R for all…

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: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

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Q: Let A = {0,1,2} and B = {-2,-1,0}. Define a relation C from A to B as follows: For any (x,y) A x B,…

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Q: For each n E N, we write S" := {(x1, x2, ..., In+1) E R"+1 : E? = 1}. (1) Let f : S2 → Rª be the…

A: Given: Sn:=x1,x2,...,xn+1∈ℝn+1:∑i=1n+1xi2=1 for each n∈ℕ f:S2→ℝ4 is the function defined by…

Q: A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x;…

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Q: Q7. Let R be a relation on the set Z defined by the following rule: for all a, b e Z, a Rb if and…

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Q: 1. Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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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 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 following relation on C\{0}: S = {(x, y) = (C\{0})² : y/x is real}. Prove that S is an…

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Q: Let R be a relation on the set of all functions from Z to Z defined by: R = {(f,9)|f(1) = g(3) or…

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Q: 5. Given a function f: A → B. Define the relation f from P(A) to P(B) by f = {(X,Y)C P(A) × P(B) | Y…

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Q: A relation R defined on the given set A will satisfy

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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: a. Define a relation R on Z as follows: For all integers m and n, mRn + 3|(m – n). Then 3R5 (A) True…

A: We have to check whether given statement is true or false.

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: Verify that the relation "... is tangent to... at a" is an equivalence relation on the functions…

A: An equivalence relation on a set S is a relation ~ on S such that: 1) x~x for all x∈S then the…

Q: et S ⊆ N, and for any a, b ∈ N, consider a relation R such that aRb if and only if there exists c ∈…

A: This is the problem of 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: 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: Define a relation C from R to R as follows: For any (x,y) R x R, (x,y)C meaning that x2 + y2 = 1…

A: Given

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

A: Definitions of symmetric, reflexive,transitive are given.We have to check them .

Q: A relation R on a set A is called anti-symmetric if O (a, b) E R implies (b, a) E R for every a, b e…

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Q: B Let A = {(x,y) |x-yeQ for x, y = R} be a relation on K. Which statement best describes problem?…

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Q: Let S be the following relation on R: S = {(x, y) = R² :y-x is rational}. Prove that S is an…

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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 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: 2. Define a relation C from IR to IR as follows: For any (x, y) E IR x IR (x, y) EC means that x2 +…

A: We will use basic definitions of relation.

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 S be the following relation on C10). S=[(x,y) E (C\[0]): y/x is real). Prove that S is an…

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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 a relation and S its reverse. Show that R is injective if and only if S is well defined,…

A: Consider the provided question, Given that, R be a relation and S its reverse. Let R is a relation…