1. Let X = {1,2, 3, 4}. A topology on X is a. T = {ø, X, {1}, {2}} b. T2 = {6, X, {1}, {3, 4}} c. T3 = {0, X, {1}, {1,3, 4}} %3D d. None of the above

Q: 2. Let (X,r) be a topological space. Where X {a,b.c,d,e} and…

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Q: Which of the following is a topology on X = {1,2,3,4} T= {4. {1}.{2}. {1,2},{3}} T = {4.X. {1}.{2}}…

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Q: Determine which of these relations are transitive. The variables x, y, x', y represent integers. A.…

A: Note: As multiple questions have been posted, so only A is solved according to QnA guidelines.…

Q: Let X: = {a, b, c}. Y: = {1,2,3,4}. Let f:X → Y, f:= {(a, 3), (b, 3), (c, 4)}. If Ty = {Ø, X, {a,…

A: Let x:=a,b,c   y:=1,2,3,4   Let f:x→yf:=a,3,b,3,c,4  if Tx=ϕ,x,a,b,aTy:=ϕ,y,1,33,431,3,4   then f…

Q: 2] -1 1] a. Find SVD from A 1. A = [4 | b. Find SVD from A invers 2. A = [; : : 8] 1 0 0 0 a. Find…

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Q: Let W = (0, 1, 3}, X = {1, 3, 5), Y = (3, 4} and Z = {(1, 2), (3, 4), (1, 3),(2, 4). Compute (X x Y)…

A: The given problem is to find the Cartesian product of given sets and verify the Cartesian product…

Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

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Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

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Q: Fix a prime number p. For x EQ - {0}, write x = p" () where a, b € Z, a and b are not divisible by…

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Q: Ex:Let (Q,0)be a slouP. A nodremp ty set HS Q - is a Sab sYou? of G if and on ly if ab" E He fer anS…

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Q: a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} a1.…

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Q: Set X is convex if

A: Given that a set X is convex if  . . . .

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: Let v = (5, 1, 2) and w = (4, –3, 6). Find each of the following: v+ w, v– 3w, || v||, || v – w ||

A: Solution: The objective is to find the required values

Q: Let S = {1,2,3, 4}. For each of the following relations on S give its transitive closure. a) {(1,1),…

A: Concept: In mathematics, the transitive closure of a binary relation R on set X is the smallest…

Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

Q: In R4, let S = span{(1, 1, 1, 1)T ,(1, 2, 1, 3)T }. Find S⊥.

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Q: 2. Let A = {a, b, c}, B = {x, y, z}, C = {r, s,t}. Let f : A → B and g : B → C be defined by: f =…

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