14. Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A→ B as follows: For all (x, y) E A × B. (x, y) ER if and only if x * y >7, Find out following: a. Rin the enumeration form b. Domain of R c. Co-domain of R

Q: Consider the set ℕ× ℕ. We will informally think of the pair (x, y) ∈ ℕ× ℕ as representing the…

A: a) The relation is defined on ℕ×ℕ as follows. x,y~n,m if and only if x+m=n+y. Every x,y~x,y since…

Q: 0,1,2

A:

Q: A relation Ris defined on N by a R b if a/b e N. For c, d e N, under what conditions is c R1 d?

A: An inverse relation is the set of ordered pairs obtained by interchanging the first and second…

Q: Let X = {x E Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1 < 15}. Define a relation R from X to…

A: We have to find the elements of X and we have to define a relation R from X to Y.

Q: Assume that you know that ~ is an equivalence relation on R\ {0} defined as follows: xy > 0. Find…

A:

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…

A:

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

A:

Q: 10.9. Determine which of the following five relations R; (i = 1, 2, ..., 5) are functions. d. R4 is…

A:

Q: C. Let T be defined onN N by (a, b)T (c, d) if and only if a c and b 2 d. Write down the full nature…

A: We will use the basic definition of reflexive, symmetric, antisymmetric and transitive realtion.

Q: on P(X), where X = Y, Z E P(X), we say Y - Z if and only if Y has the same number of ele- Define a…

A: Given a set X={1,2,3,4,5,6}. Define a relation ~ on P(X) as : For Y,Z∈ P(X), we say  Y~Z if and only…

Q: Let R=}(x,y)|2 divides 8x+by} be a relation the Set H= {1, 2,3.4,5, 6. 10 Determine whether the…

A:

Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: %3D For all (x, y) E A × A, (x,…

A:

Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all (x, y) ∈ A…

A: A=3,4,5B=1,2,3,4R=x,y: x∈A, y∈B ∋xy&gt;7 a. R=3,3, 3,4, 3,5, 4,2, 4,3, 4,5, 5,2, 5,3, 5,4, 5,5

Q: 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 = y –q…

A: 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 = y –q…

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

A:

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: Give the relation R induced by the partition above on A.

A:

Q: Let G = {-2,0, 2} and H = {4,6,8} and define a relation V from G to H as follows: %3D For all (x, y)…

A: Solve the following

Q: Let R be the relation on R defined by R= {(x, y) E R × R | x² + y² = 4 or x = y²}. Answer each of…

A: Given that R be the relation on ℝ defined by,R=x,y∈ℝ×ℝx2+y2=4 or x=y2

Q: T is a function?

A:

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

A:

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: Consider the relation S on N defined by uSy⟺5|(y+u). Is it reflexive?

A: No it is not a reflexive 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: 2. Consider the relation on the natural numbers N defined as follows: for all x, y e N, xRy if and…

A: According to question,We have to discuss about reflexive, symmetric, transitive relation.

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: 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: 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: Q1 Given a relation R on Z defined by mRn7|(mn) for all m, n € Z. Find the equivalent class…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 9.15. A relation R is defined on Z by a Rbif |a – b| < 2. Which of the properties reflexive,…

A: Given : A relation is R is defined on Z is given by  a R b if a-b≤2  Which of the properties…

Q: Let R be a relation from X to Y and S be its reverse relation from Y to X. Prove or disprove that R…

A: According to the given information it is required to prove/disprove that R is injective and well…

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: Let C = {a, b, c, d}. Find a relation R on C that has exactly 3 ordered pair members and is both…

A:

Q: Define a relation T on R by xT y if and only if (sin^2) x + (cos^2) y = 1. (a) Prove that T is an…

A:

Q: Let D = {2,4,6} and E = (1,3,5}, define a relation R from D to E as follows, given that…

A:

Q: Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2]…

A:

Q: A relation R is defined on Z by xRy if x*y >= 0. Prove or disprove the following: a. R is…

A: Let us consider the given relation R on set X. R is said to be reflexive for any x in X, x R x. R…

Q: A relation * is defined on the set R-{0} by x * y if and only if xy > 0. For each of the following…

A:

Q: Let R be a relation on Z defined by xRy if and only if x-y=7k for kEZ. The equivalence class of [5]…

A:

Q: 2. Let H ≤ G and define = on G by a = b iff a¯¹b € H. Show that =µ is an equivalence relation.

A:

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 = {2, 4} and B = {1, 3, 5} and define rela- tions U, V, and W from A to B as follows: For…

A: (a) First obtain the 3 relations as follows.

Q: The relation xy >= 1 where x,y are on the set of all integers is reflexive. True False

A: Given relation xy≥1, where x,y are on the set of all integers

Q: In this exercise, you want to show that a relation RC A? is transitive + R"C R for all n E N = {1,2,…

A:

Q: Let R be a relation defined on Z by xRy if and only if x-y=7k for kez. The equivalence class of [5]…

A: Given relation is xRy iff x-y=7k So, equivalence class of 5 will contain ....-9, -2, 5, 12, 19,....…

Q: Let X = {x € Z+ | 15 < 4x < 22} and Y = {y is even | 0 < 2y +1< 15}. Define a relation R from X to Y…

A: ANSWER ONLY ASAP! What are the elements of the Cartesian product X x Y?

Q: a L4 D 2 of 5 disprove that R is a partial order : {(a,b) : 3keza = k * b} be a relation over the…

A:

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: Given C = {1, 2, 3, 4}. We find a relation R on C that has exactly 3 ordered pair members and  both…

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:…