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, y) E S if and only if that x – y > 2. a. Is 3 S 4 ?

Q: 2. Let X be a set, and let A C X. Define a function f: P(X)→ P(X) by f(B) = AUB for all BE P(X).…

A: Given: 2) Here the given is im(f) = f(A)  A ∈ P(X) = C∈P(X)  A ⊆C, We have to show that im(f) =…

Q: Suppose that the functions u and w are defined as follows. u (x) = 2x+1 w (x) = -2x2 Find the…

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Q: Let E = {1, 2, 3} and F = {-2, –1, 0} and define a relation T from E to F as follows: For every (х,…

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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: Let X and Y denote be as follows: E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) =…

A: Given data E(X) = 10, E(X2) = 125, E(Y) = 20, Var(Y) =100 , and Var(X+Y) = 155.  W = 2X-Y and  T =…

Q: Vx E X, (x, x) ¢ R. X = {1,2,3}, h of the following relations R on X is irreflexive?

A: Here given set   X={1,2,3}   we know that relation is irreflexive when each x belong X (x,x) dose…

Q: Suppose that x, y, z are functions of the independent variables u, v, w. Which of the following…

A: It is given that, x,y,z are a function of the independent variables u,v,w. Here we have to find…

Q: Suppose that the functions u and w are defined as follows. u (2) =+6 w (x) =/x+1 Find the following.…

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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…

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Q: Given that there exists a surjective function f : S → T, which of the following substitutions for…

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Q: Consider the function d: R² × R² → R defined by min{|y2 - x₂, 1} if x₁ = y₁ otherwise, d(x, y) :=…

A: A metric on a set X is defined as a function d: X×X→R which satisfies the following conditions:…

Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

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Q: Suppose that the functions u and w are defined as follows. u (x) =-x+2 w (x) = -2x? Find the…

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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: Let the relation S defined as S = {(x,y) | y = X2 + 4x +3}. What is the domain of S?

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Q: . Define a relation from Z to Z as follows: For all x EZ and all y E Z, x and y are related iff y =…

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Q: A on S is a function from S×S into S.

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Q: Given a function f: A → B and subsets X,Y C B, prove that f"(XNY) = f(X)nf-(Y).

A: He we will prove the given result.

Q: Let X = {a, b, c} and Y = {1, 2, 3, 4}. Which of the relations A, B, c defined below are functions…

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Q: Suppose z = z(x,y) is x + y+z = e¬(x+y+z) , then which relation is correct? az D): az az az az 1 ду…

A: The solution is given as follows :

Q: (a) Show that the formula (VæR(g(x), x) = Vx3yR(y,x)) is universally valid, where g is a 1-place…

A: Part(a): As we know, ∀xRgx,x⇒∀x∃yRy,x Where g is a two place function symbol and R is a two place…

Q: Let A = {0,1,2} and B = {-2,-1,0}. Define a relation C from A to B as follows: For any (x,y) A x B,…

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Q: Determine x(n) from the following x(z) taking in account two cases of x(n) as a causal and a non-…

A: Given that  x(z) = (z+1) /( (z-0.5)(z-1)^2) We have to determine x(n) from the following x(z) taking…

Q: For each n E N, we write S" := {(x1, x2, ..., In+1) E R"+1 : E? = 1}. (1) Let f : S2 → Rª be the…

A: Given: Sn:=x1,x2,...,xn+1∈ℝn+1:∑i=1n+1xi2=1 for each n∈ℕ f:S2→ℝ4 is the function defined by…

Q: i). Find the highest normal form of a relation R(A,B,C,D,E) with FD set as (BC->D, AC->BE, B->E}

A: As we can see, (AC)+ = {A, C, B, E, D} but none of its subset can determine all attribute of…

Q: 2. Compute P, and Py as a function of x, y, P.

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

A: A relation defines the relationship between sets of values of ordered Paris. The set of elements in…

Q: 5. Given a function f: A → B. Define the relation f from P(A) to P(B) by f = {(X,Y)C P(A) × P(B) | Y…

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Q: 2. Let a = (a1,..., an) € R" and let f : R" →R be defined by f(x) = (a, x). Compute the following:…

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Q: Let s(x) and c(x) be two functions satisfying s′(x) = c(x) and c′(x) = −s(x) for all x. If s(0) = 0…

A: Given, s′(x) = c(x) and c′(x) = −s(x) for all x. If s(0) = 0 and c(0) = 1, To prove:     [s(x)]2 +…

Q: Define F: Z × Z→Z×Z as follows: For all ordered pairs (a, b) of integers, F(a, b) = (2a + 1, 3b –…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose that the functions u and w are defined as follows. u (x) = 2x+2 w (x) =x² – 2 Find the…

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Q: Let E = {1, 2, 3} and F = {-2, –1, 0} and define a relation T from E to F as follows: For every (х,…

A: Since you have posted multipart question and we can answer three subparts. So, answering the first…

Q: Suppose that the functions u and w are defined as follows. u (x) = 2x+2 w (x) =x²-2 Find the…

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Q: 7. If a functionf defined in [a, b] is such that o (i) f is derivable in [a, b], (ii) f' (a) and f'…

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Q: Let X be a nonempty set and fix x E X. Define (1, rE A (A) = 10, 4 A

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Q: Suppose that the functions u and w are defined as follows. u (x) =x²+5 w (x) = /x+7 |D Find the…

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Q: Let f(x) = x² and let P = { -3, -5/2, -2, -3/2, -1, -1/2, 0 }. Compute Lf (P) and Uf (P). Lf (P) =…

A: We have to fid the Lf(p) , Uf(p)

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…

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Q: Define a relation S from R to R as follows: For every (x, y) ER X R, (x, y) E S means that x> y. a.…

A: (a)It is given that the relation S from R to R is defined as for every (x, y) ϵ R × R, (x, y) ϵ S…

Q: Suppose that the functions u and w are defined as follows. u (x) =x² +5 w (x) = /x+7 %3D Find the…

A: Given, ux=x2+5wx=x+7

Q: A relation R on a set A is called anti-symmetric if O (a, b) E R implies (b, a) E R for every a, b e…

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Q: If S. F.dr is independent of the path C joining any two points, show that there exists a function O…

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

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Q: Let f(x, y) = e*,4 Evaluate f(4, 3)

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Q: 3. Eliminate B and a from the relation x = Bcos(wt + a) in which w is a parameter not to be…

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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: Determine whether the following relation is a function from R into R. A Iso deter- mine whether that…

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Q: 14,497 where y is the 55000 and older with at least a indicates a linear relation nt of 0.7581.…

A: Note:As per the requirement of the students solving part(c). Let Y= a+bX be the regression line.…