Activity 1. A Relation as a Subset Let A = {1,2} and B = (x, y) E Ax B, {1,2,3} and define a relation R from A to B as follows: Given any (x, y) ER means that is an integer x-y A. State explicitly which ordered pairs are in A X B and which are in R. B. Is 1 R 3? Is 2 R 3? Is 2 R 2? What are the domain and co-domain of B2

Q: True or False? 11. If Γ = {[0, 1/n) | n ∈ N} then ∩Γ = [0, 1). 12. Let R be a relation on a set A.…

A: 11) if Γ ={[0,1n) | n∈N}  then ∩Γ=[0,1)         Γ= {[0,1), [0,1/2), [0,1/3), [0,1/4), [0,1/5),…

Q: from A to B as follows : Given any {x y} e Y xZ. (x, y) e R means that x + y_is an integer. 2 1.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: b) Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A as follows: For every (x, y ) еА,…

A:

Q: 4. a) Define the following terms: i) POSETS ii) Equivalence relation ng the relation R and S on

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 3 Let A = {0, 1, 2,3} and B = (0,1, 2, 4, 5, 8, 9}. Define a relation R from A to B as follows: for…

A: A=0,1,2,3 and B=0,1,2,4,5,8,9A relation R from A to B,x,y∈R if and only if x+1=y2

Q: Let R be the relation defined on Z by aRb it a+b is even Find the number of distinct classes? Select…

A: aRb if and only if a+b is even. a and b are integers. Hence, Either a and b both are even or both…

Q: 3. a. If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows:…

A:

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) ,…

Q: Q 6 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,…

A:

Q: Let A={1,2,3} and B={-2,-1,0}. Define a relation R from S to T as follows: For all (x,y) in AxB,…

A:

Q: 7. Suppose yo 70 is fixed. Find a geometric description of {u+ iv 1 :x ER x + iyo that is, the image…

A: Lets suppose that w=1/z be the transformation where w=u+iv and z=x+iy   Now we will find the images…

Q: 5. Suppose R is a relation on a set A. The inverse relation R-1 is defined by letting a R-1 b if b R…

A:

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

A:

Q: Question 10 A relation R on the set A is irreflexive if for every a E A, (a, a) ¢ R. A relation R on…

A:

Q: Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A…

A: We have to answer the following questions :  (a) Find the equivalence class  -35 (b) Find the…

Q: 6. Let A {1,2, 3, 4, 5} and define a relation on A as follows: For all x, y E A, %3D xRy + x+ y is…

A:

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows:…

A:

Q: Consider the recurrent relation: An = An-1 + 4 n2 0, A1 = 0 %3D a. The given definition is correct…

A:

Q: d) Give an example of a relation that antisymetric. Your text defines antisymmetric as "A relation R…

A: Given that, Let C=x∈Z: x≡7 mod 9 and D=x∈Z: x≡1 mod 3 Give an example of a relation that is…

Q: b) Let C = {1, 2, 3, 4}. Find a relation R on C that has exactly 3 ordered pair members and is both…

A:

Q: + x* - y| > 20. Examine R for Consider a binary relation R on set S = {2, 3, 5, 9, 11, 13} defined…

A: Let R be a  binary relation on a set A R is reflexive if  aRa , ∀a∈A otherwise the relation is…

Q: 11. Let C= (0, 1, 2) and D= (2,4, 6, 8) and define a relation R from A to B as follows: For all (x,…

A: We have to determine the above terms for the given relation.

Q: Why

A: The given relation  R={(3,3),(4,4),(6,6),(7,7),(3,6),(6,3),(4,7),(7,4)}

Q: 5. Let R be a relation from the power set P(X) to itself, where X = {1,2,3, 4}, defined by A R B if…

A:

Q: 5. Define a relation Sfrom R to R as follows: For all (x, y) ERXR, (x, y) E S means that x 2y. a. Is…

A:

Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

A:

Q: b) Let S = { (x, y) | x, y € R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

A: We have S=x,yx,y∈R x,yRp,q  if and only if x-p=y-q   Reflexive property: A relation R is said to be…

Q: 4. Let Let A={2,4} and B={1,3,5} and define relations U,V, and W from A to B as follows. For all (x,…

A:

Q: Part II: Prove/Disprove the following 2. Let R be the relation on Z, defined as follows: Vm, n e Z,…

A:

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A:

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula.…

A: Solution:   This is an equivalence relation since:A U Y = A U YA U Y = B U Y implies that B U Y = A…

Q: 1. Let A = (2, 3, 4} and B = {6, 8, 10) and define a relation R from A to B as follows: For all (x,…

A: Relation

Q: 4. Let G = {-2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows: For all (x,…

A:

Q: (3) Let A={1,3,5,7}, B={0,4,8}. Define the relation R as: For all x E A and y E B, xRy , if and only…

A:

Q: ction 1.3: Let A = {-2, –1,0, 1, 2} and B = {1,2,3,5}, and define a relation R from A to B as lows:…

A:

Q: 5. Let A={4, 5,6} and B= {5,6,7} and define relations R,S, and T from A to B as follows: %3D For all…

A:

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: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: 8. Let A (2, 4) and B (1,3, 5) and define relations U, V, and W from A to B as follows: For all (x,…

A: Given that: A={2,4}B={1,3,5}

Q: Let A={1,2,3} and B={-2,-1,0}. Define a relation R from S to T as follows: For all (x,y) in AxB,…

A: We will find out the required values.

Q: 1. Let A (2,3,4) and B= (6,8,10) and define a relation R from A to B as follows: For all %3D (x, y)e…

A: Basic properties of sets and relations can be used to find the answer to this question keeping in my…

Q: Let A={5,6,7,8,9,10,11} and define a relation S on A as follows xS y 3|(x-y) (a) Is 5S7? Why? (b) Is…

A:

Q: 4-part question: Let R be a relation from A to B and S a relation from B to C.  (a) Define the…

A: As there are given four  questions hence I do only first three.   (a) we have three sets A, B and C;…

Q: Answer All Questions Please.

A:

Q: (a) Let R be the relation on Z defined as follows: For a, b € Z, a~b if and only if a is a multiple…

A: a) R be the relation on ℤ defined as follows:       a,b∈ℤ, a~b if and only if 'a' is a multiple of…

Q: {cat, dog, bird, rat} and R be a relation on A defined by :x and y have at least one letter in…

A: 2. a. First we now write the relation on A as form of matrix as follows which is also the adjacency…

Q: Question Number 06 a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive,…

A: A relation R on a set A=1,2,3,4 is defined by  R=1,3,1,4,2,3,2,4,3,1,3,4 The relation R is reflexive…

Q: 11. Let C= {0, 1, 2} and D= [2, 4, 6, 8) a relation R from A to B as follows: For all (x, y) E AXB,…

A: Given  :-  Let C =  0 , 1 , 2  and D =  2 , 4 , 6 , 8  and define a relation R from A to B as…

Q: 7. Suppose yo 70 is fixed. Find a geometric description of 1 {u+ € R} + iv :x x + iyo that is, the…

A:

Q: 6. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Answer for sub question a: Given A=9,11,12,14, B=1,2,3,4. The relation R:A→B is defined as follows:…