For any set A and B prove that: a) А - В %3D А - (ВПА) b) BC A' iff A n B = ¢ с) (А — В) U В %3D Aiff B с A

Q: Prove that if a, bER and a < b, then |(a, b)| = |[a, b)| = |(a,b]| = b – a. %3D %3D %3D

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Q: If {x, y} and {z, w} are both linearly independent sets in R^n, then {x, y, z, w} is also linearly…

A: Answer

Q: Exercise 2. Show that if B + Ø then dom(A × B) = A. %3D

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Q: Show by any valid method except Venn diagram that ((A U D) N B)n ((C U B) N A) = AN B. %3D

A: Given: A∪D∩B∩C∪B∩A We have to prove A∪D∩B∩C∪B∩A=A∩B

Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

A: Given four points are  P(2,1,1)Q(1,3,2)R(2,1,3)S(3,2,0)

Q: Complete the proof: If A≤B and B≤C, then ACCn(transitive property for set in inclusion) Need to…

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Q: Find a universe for variable x,y,z in which the statement ƎxƎy∀z((x=z)or (y=z)) is true and another…

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Q: The projection of u onto v is given by projvu = ________.

A: The projection of u onto v is given by projvu = compvu.

Q: Show that an infinite intersection of closed sets F, k = 1, 2, 3, . .., in a metric space (S, d) is…

A: first we will proof that an infinite union of Open sets in metric space ( S, d) is open using the…

Q: Let u, EC prove that ū · v = v · ū น

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Q: O Show that if Si and S2 are convex sets in R™X", then so is t mxn S = {(x, y1 + y2) | x € R", y1,…

A: Convex set: , If a and b are points in a vector space S. Then the vector space is called convex set…

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: 3.5 Show that the metric space (R, d), where d(r, y) = |x – y|, is separable.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Write a flow proof, Use the information from the diagram to prove that A ABD A CDB. A ....

A: Given:

Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: 1. Prove that for all sets X, Y , if XU Y = Xn Y, then X = Y. %3D

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Q: 3. If U and V are such that u; ='x; – A, v; =y, - B, then Cov (U, V) is :

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Q: Let a1, a2 and a3 be colums of A, i.e A = [a1,a2,a3] and let W = span {a1,a2} compute projw a3.

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Q: If p = (u, v, w), show that Ipl < lul + |미 + |wl а. b. Ju| < \pl, ]v] < \pl, ]w] < \pl.

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Q: Consider the set S = {zeC:0< Re(z) < 2 & 0<Im(z) < 3} What is its interior? {zeC:0<Re(z) < 2 & 0<…

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: a subipace of Masa And, the set s-{(:),(;:), () #) w {():x, YaR} i) W = {Ğ ): x, Question 3 -{:9),(?…

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Q: Given that x, y, and z . Prove that if (x^2)|y and (y^3)|z, then (x^6)|z

A: Solution: The objective is to prove that the given statement

Q: . Use a two-column proof to prove the equivalence below -(PV-Q) v (-P A-Q) = ¬P

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Q: 1. What congruence postulate/theorem cannot be used to prove that ALIV AJIN given that LVis parallel…

A: topic- congruent triangles

Q: |- Extends the set S={(-44,4} basis tor IR. to %3D

A: Basis of a vector space problem...

Q: If A = 2x²,-3yz, xz² and qp = 2z - x³y. Evaluate A Vop and A x Vp at the point (1, -1, 1).

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Q: *10. Suppose AB = CD, AB 1 BC, and CD I BC. (a) Why must AC BD? (What congruence criterion…

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Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: The greatest common divisor c, of a and b, denoted as c = gcd(a,b), is the largest number that…

A: Here is the solution

Q: Show whether the sets are connected or not. 1. {z € C | 1< ]z| < 2} 2. D(0, 1) U D(2i, }),

A: 1. Given: D⊂E⊂A then D=E    To Find: To whether the sets are connected.   Where z=x+iy           z…

Q: Prove that if A is skew-symmetric matrir, Q = et is orthogonal.

A: c) To prove:- If A is skew-symmetric matrix , Q=eAt is orthogonal. Proof:- Ais skew-symmetric matrix…

Q: for fuzzy sets A, B and C, (AVB)vc = AVIB VC). (Ал в) лс - АЛ(ВЛС). (A V BF = A“AR prove that AA CB…

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Q: With help of Venn diagrams show that the following are indeed true: a.X n (Y U Z) = (X n Y) U (X…

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Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: Suppose a, = lan 1- 6an 2 + lan 3 and a4 = 47, as = 3, and a6 = -273. Find a1, a2, and az. %3D %3D =…

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Q: 1. For n 2 2, let A = [a E M,(C). Suppose A is diagonally dominant. Show that if af # 0 for all i,…

A: We will use the basic knowledge of matrices and diagonal dominance to answer this question in…

Q: Let a and b be two elements in a lattice (A, ≤). Show that a ˄ b ˂ a and a ˄ b ˂ b if and only if a…

A: Suppose that a∧b&lt;a and a∧b&lt;b. To show that a and b are incomparable assume the contrary that a…

Q: (iii) If (X,r) is topological space, A,BCX. Prove that (a) b(A)=AA (b) If ACB, then d(A) ≤d(B)

A: First part Is obvious from definition of boundary points of a set.

Q: et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions…

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Q: Exercise 2 Given KB = (X→Y) ^ (Y→Z), and a = (X→Z) Is KB |= a is valid or not?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Given   KB = (X→Y) ∧  (Y→Z), and   α  = (X→Z) Is KB |= α is valid or not?

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

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Q: Prove that  Two lattice points (a,b) and (m,n) are mutually visible if and only if a−m and b−n are…

A: Given theorem is  Two lattice points (a,b) and (m,n)  are mutually visible if and only if a−m and…

Q: 1/ For any. topological space (X, T), if T has only three elements then (X, T) is connected.

A: Given: Topological space X, T and T has 3 elements  To prove that X, T is connected when T has 3…

Q: 3.3 Let 11 and ra be distinct points in the metric space (S, d). Verify that there are open balls…

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Q: If A = {1,2,5,8, 9} and R = {(x, y) E A X A 3 x + 1 = y}, S = {(x, y) E A X A 3 y +1 = x} %3D %3D…

A: SOLUTION-