Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R = IdA, then S is surjective. If the assertion is not true, find additional assertions that will make it true.

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: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: Consider the following relation R on R: (x, y) ER if and only if y E Q. What are the properties of…

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Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. Is R reflexive?…

A: Given:  R is a relation defined on P 1, 2, … , 100 by A R B  if and only if A ∪ B is even. We have…

Q: Fuppose that the relation R indicates whether c articular student is registered for a particular c…

A: In this question, the concept of Relation is applied. Relation The relation is a relationship…

Q: Disprove that for any relations R and S, ran(S • R) = ran(S).

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Q: Let R be a relation on R × R such that (,71)R¢xI2) if and only if xıyı = x2y2. -) Is (2.3)R(1,-6) a…

A: It is given that R be a relation on ℝ×ℝ such that Rx2,y2x1,y1 iff x1y1=x2y2 For part (a) According…

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

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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: 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: 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: Consider a relation ~ on the set Z such that x~y if and only if x + y is even. The relation ~ is…

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Q: 3. Let R be the relation defined on P({1,..., 100}) by ARB if and only if |AU B| is even. Is R…

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Q: Which of the following is/are true for the relation R, where a is related to b (aRb), if and only if…

A: Suppose, A be any set and suppose R:A->A is a relation. Then, R is reflexive: if for every x in…

Q: Consider the relation S on N defined by uSy + 5|(y + u). Determine whether S is symmetric, reflexive…

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Q: (b) Let - be the relation on C defined by z ~ w if and only if z + w e R. Proye that is an…

A: This can be solved as follows:

Q: Let R be the relation on the set of people with doctorates such that (a, b) ER if and only if a was…

A: Let A be the set of all people with doctorates and R be a relations on A defined by a,b∈R if and…

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: Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: Given :-

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: 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: 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: Let : [0, 1] → [0.c], te- and let w be a 1-form on R. What and foe, and why? is the relation between…

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Q: 5. For each of the following relations, indicate whether the relation is reflexive, anti-reflexive,…

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Q: 5. Let A = {1, 2} and B x+y y) e R such that {3,4}and define a relation from A to B as (x,y) e AxB…

A: We will find out the required values.

Q: A relation R is defined on Z by a R b if |a – b| < 2. Which of the properties reflexive, symmetric…

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Q: b( Let S be the relation defined on P ((1, 2, 3, 4}) defined by X SY if and only if IX| = |Y| (mod…

A: The complete solutions are given below

Q: Let the relation R on the set Z be given by the condition: (x, y) E Rif and only if x4 = y4. Answer…

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Q: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

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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: 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: Consider the relation on Z × Z given by aRb if a &lt; b. Is R transitive. Answer yes or no…

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Q: A relation R on a set A is backwards transitive if, and only if, for every r, y, z E A, if rRy and…

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Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} issymmetric but neither…

A: Given, relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)}.

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 S be the following relation on C: S = {(x, y) = C²:y-x=bi for some real number b}. Prove that S…

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Q: A relation R is defined on the set, Z, of integers by xRy if and only if x+ y 2 5. R is A reflexive…

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Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

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 R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

Q: Suppose there are two transitive relations R, S Disprove the claim that the composed relation S R…

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Q: Let R be the relation defined on P({1,.…, 100}) by ... ARB if and only if |AUB| is even. Is R…

A: Relation: - A subset of the productA× B could be a relation R from a non-empty set A to a non-empty…

Q: Define a relation R from R to R as follows: For all (x, y) ER×R, (x, y) eR if, and only if, x = y? +…

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

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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…