Let ‘E’ & ‘F’ are any two non-empty sets and there order are as follows;                                  let ;  | E |  = s     and  | F |    = t                           What is the order of its cartesian product.

Q: Let A = { 2, 3, 4 } and B = { 6, 8, 10, 12 } and define a relation R from A to B as follows: %3D For…

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Q: Let A be a nonempty set and let R1 and R2 be equivalence relations on A. For each x E A, describe [x…

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Q: Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also reflexive? Is R1 ∩ R2…

A: Let A be any set with  symmetric relations R1 and R2 defined on it. Hence R1 and R2 be subset of…

Q: Let A be a set and let a € A. Suppose that f: A→ A satisfies (a) a = f (a), (b) if x Ey then f (x) =…

A: Given: f:A→A a) a∈fa b) fx∈fy To find: Solution

Q: 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 | y.…

A: A= 2,4,6,12,16,18,24,32 R is define as xRy if x/y  so, R = (2,2) (2,4), (2,6) (2,12) , (2,16) (2,18)…

Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

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Q: Let R be an equivalence relation over set A. Let a and b be any two elements in A. a) Prove that (a,…

A: Given that R is an equivalence relation over the set A and a and b are any two elements in A. Since…

Q: 2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation…

A: A relation is a subset of Cartesian product of two sets. Therefore, every element in a relation set…

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: Let ∅ be the empty set. Let X be the real line, the entire plane, or, in the three-dimensional case,…

A: Given:

Q: Show that the relation R = ∅ on a nonempty set S is symmetric and transitive, but not reflexive

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Q: Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R).…

A: Given A be a set and R and S be relations on A. R+S on A is defined by R+S=R-S∪S-R=R∪S-R∩S=R∪S∩R∩Sc…

Q: (5) Let ƒ : A → B and g : B → C, where f and g are functions and A, B, and C are sets. (a) Prove…

A: In 2 nd part construct a function

Q: Let R be the relation defined by x R y x² < y² Determine if R is an order relation on N? on Z?…

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Q: Let S be the following relation on R\{0}: S = {(x, y) = (R\{0})2: y/x = 2k for some integer k}.…

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Q: (i) The equivalence class [b] determined by b E B is a non-empty set. 1 (ii) If r and y are elements…

A: Given that S and T are equivalence relation on a set B. i ) the equivalence class [b] determined by…

Q: Let X = {6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z e N₁ x + z = y}, where…

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Q: Let S' = {x € R² : ||x|| = 1} C X. and endow S' with the same equivalence (b) relation - as above.…

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Q: Consider the binary relation R defined on (N* x N*) by: V (X1. Yı). (x2. Y2) E N* x N*, (x1. Yı) R…

A: Order relation (definition)-: A relation R is called an order relation if it is reflexive,…

Q: a)Let A = {x ∈ R + : x 2 < 2} . Explain why A i bounded above and below and find sup(A) and inf(A).…

A: A can be written in interval form

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: Let A be a set and R and S be relations on A. Dene the relation R + S on A by R + S = (R-S) […

A: Let A be a set and R and S be relations on A. Define the relation R + S on A by R + S = (R-S) ∪…

Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

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

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: 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: Let R be the relation on the set of real numbers such that x R y if and only if x and y are real…

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Q: A) Let A = {2,3, 6, 12, 24, 36, 72} and <a relations on A such that a <b+ a[b Determine whether \(…

A: A lattice is a poset in which any two elements have a meet and a join. Draw the Hasse diagram.

Q: Let R and I be equivalence relations on a nonempty set A. Then for all r, y E A, [a]ang = [r]an[v]s.…

A: 3. Given that R and P be equivalence relations on a nonempty set A. Then for all x, y∈A,  xR∩P=xR∩yP…

Q: 6.3. Let (A, <A) and (B,<B) be two partially ordered sets. One can define on the cartesian product A…

A: Given: A, ⩽A and B, ⩽B are partially ordered sets.  A Cartesian product A x B is defined with…

Q: 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 =…

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Q: Let S be the following relation on R\{0}: S = {(x, y) = (R\{0})² : y/x = 2k for some integer k}.…

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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: Let A and B be sets. Show that               f : A × B → B × A such that                  f(a, b) =…

A: Given:

Q: f relations R and S on Z such that (a) Both R and S are not equivalence relations but R + S is. (b)…

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Q: '17. Prove or disprove: Let R be an equivalence relation defined on a set A. For any x, y E A,…

A: Given result is: '' Let R be an equivalence relation defined on a set A. For any x,y∈A, either x∩y=∅…

Q: Denote by Z, the set of nonnegative integers. Let Rbe the relation on A = R defined by x Ry if x – y…

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Q: State whether each of the following statements is true or false. Then give an explanation, proof or…

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Q: 5. Let a and b be real numbers, not both zero. For (x1, Y1) and (x2, 42) in R², (x1, yı) ~ (x2, y2)…

A: Given that,  a and b are real numbers, not both zero. For By using the definition of equivalence…

Q: 13. Let R C R XR with {(x, y)|x2 =, y?}. Characterize R in terms of whether it is reflexive,…

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Q: 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 =…

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Q: 6. (a) Let ~ be the relation on Mat2(R) defined by: A ~ B if and only if the (2, 1) entry of A – B"…

A: This problem can be solved as follows:

Q: Let A De a set and ns Ol A. Che R+S = (R – S)U (S – R). Show that: (b) but R+S is countable. Show…

A: Given A be a set and R and S be relations on A. A relation R+S on A is defined by R+S=R-S∪S-R Let…

Q: R How to prove that " If is the equivalence B relation on the set and is the function R = IB then

A: given in question R is a equivalence relation on set B that means R is reflexive ,transitive  and…

Q: Let S be the following relation on C: S = {(x, y) = C²:y-x is real}. Prove that S is an equivalence…

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

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Q: Let R be the relation on N defined by a R b if either a | 2b or b | 2a. Is R an equivalence…

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Q: Give examples of relations R and S on Z such that (a) Both R and S are not equivalence relations but…

A: (a) Let R and S be two relations on ℤ such that both R and S are not equivalence relations. Let…

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

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Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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