1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m eny oro hoth roffovizo ond Crmmotrio?

Q: 5. Define a relation S from R to R as follows: For all (x,y) ERx R, (x,y) €S means that x > y. a. Is…

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Q: 9.3. Let A = {0,1}. Determine all the relations on A.

A: The objective is to determine all the relations on A.

Q: 2. Define the sets X = {1,2,3} and Y = {4,5,6}. Now, define the relation R from X to Y by „R, if and…

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Q: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

Q: 13 - Let A={0,1,2,3} and R be the following relation on A: R= {(0, 0), (0, 1), (O, 2), (1, 0), (1,…

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Q: 1. Let A= {5,6,7,8,9,10} and define a relation S on A as follows xS y→ 2|(x-y) (a) Is 5S 6? Why? (b)…

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Q: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: Let A={5,6,7,8,9,10} and define a relation S on A as follows xSy 2|(x-y) (a) Is 5S6? Why?

A: Consider the provided question,

Q: 14) For each of the following relations on the set {1, 2, 3, 4}, decide whether it is reflexive,…

A: The solution of the problem is given in the next steps.

Q: Let Asfl,2,3} and The relations Ri=f(),(2,),(3,2) | find the following Ye lations

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Q: PROBLEM 30. For (x, y) and (u, v) in R2, define (x, y) ~ (u, v) if x² + y² = u? + v?. Prove that…

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Q: Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)}…

A: we have given relations R and S on {a, b, c, d} and we need to find composition R∘S

Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…

A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…

Q: 12. Consider the following relations on {1, 2, 3, 4). R1 = {(2,2), (2,31.2,4).(3,2).(3,3).(3,4)} R2…

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

A: (NOTE- The relation R should be from Y to Z instead of A to B.) Given sets are, Y=0,1,2 and Z=0,1…

Q: 1. Let F be a nonempty family of transitive relations. Prove that NF is a transitive relation. Hint.…

A: Given that the F be a nonempty family of transitive relations.

Q: Let

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Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

Q: 4) The relationk onthe Selof real numbers Risa partialorder relation.

A: relation R on a set A is called a partial order relation if it satisfies the following three…

Q: The relation by a = b (modn) is Partial Order Relation Ture O False O

A:

Q: 4. Suppose Rand S are symmetric relations on a set A. Prove that RoS is symmetric iff Ro S = So R.…

A: Suppose R∘S is symmetric Let s, r∈S∘R ⇔r, s∈R∘S⇔s, r∈R∘S ( since R∘S is symmetric)  So, R∘S=S∘R

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

A: Using relation property,

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: The participation of relation R can be: total, partial, onto, and into. Given A = {1, 2, 3, 5} and B…

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Q: 4.4.5 Write out the following relations as subsets of the Cartesian pod (a) The relation on N…

A: (a) The relation given is already a subset of the Cartesian product N x N. It can be written as…

Q: 1 If MR =: 1 lo 1 1., then the relation ol 1 Ris Reflexive Transitive Anti-symmetric Symmetric

A: To find: The type of relation R. Concept used: Reflexive: If all the diagonal element of MR is 1,…

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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Q: Question 6 For each of the relations on A ={1, 2, 3} below, {(1, 1), (1, 3), (3, 3)}, R = S = {(1,…

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Q: (b). Let Y = {a, e, o, i, u}, take two relations R and S on Y and Prove that (SoR)-1 : R-1os-1.

A: composition of relations

Q: If R, T, G,H are relation on A and RET,GCH then, 1. RoG CTOH 2. Тон с RoG 3. RoT S Goн 4. RoH E ToG…

A:

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

Q: Let S be the set of integers. If a, b E S, define aRb if ab >= 0. Is R anequivalence relation on…

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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: 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: Question 6 For each of the relations on A ={1, 2, 3} below, R= {(1, 1), (1, 3), (3, 3)}, S = {(1,…

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Q: on K³defined by: (a, b, c) ~ (d, e, f) if and only if ak e K – {0} such that (a, b, c) = k(c, e, d)…

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Q: O Let X = {1, 2, 3, 4, 5}. How many relations are there on X with the property that for all x E X, x…

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

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: et A={1,2} and B={1,2,3} and define a relation R from A to B as follows: •Given any (x,y) element A…

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Q: Let S = {0, 1, 2, 4, 6}. Test the following relation whether it has equivalence relation on S. R =…

A: Given relation R = {(0, 0), (1, 1), (2, 2), (4, 4), (6, 6), (0, 1), (0, 2), (1, 2), (4, 6)} on  S =…

Q: 1 Recall that for x, y ≤ R, |x − y| ≤ Rf is the absolute value of x - y. That is, if x-y≥0 |x - y =…

A: Please see the below picture for detailed solution.

Q: 3. Suppose that we have the following four tuples in a relation S with three attributes ABC:…

A: Given: Let us consider the four tuples, ABC:1,2,3,4,2,3,5,3,3,5,3,4. Let's determine the…

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: Our universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example,  R(3,-2)…

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Q: 7.1.6 For the relation R = {(x, y) : x < y} defined on N, what is R-1, and what is the intersection…

A: The detailed solution is as follows below:

Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below