Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * (X, T) is not Hausdorff but it is connected (X,T) is not connected but it is Hausdorff (X, T) is neither Hausdorff nor connected (X,T) is Hausdorff and connected

Q: If p = (u, v, w), show that Ipl < lu + |e| + |w미 а. b. Ju| < \pl, \v] < \pl; |w| < \pl.

A: (A) (|u|+|v|+|w|)2 = |u|2 + |v|2 + |w|2 + 2|u||v| + 2|v||w| + 2|w||u|…

Q: Surface of a sphere is a two-dimensional Riemannian space. Compute the Chrtstoffel symbols.

A: Given: Surface of a sphere is a two-dimensional Riemannian space To find: Chrtstoffel symbols

Q: Given r = {(0,0), (0, –1), (1, 1)}, select all true statements. Orl = {(0,0), (–1, 0), (1, 1)} OD,-1…

A: topic - functions and inverse functions

Q: A set W is defined as consisting of all the planes in R^3 that are parallel to the plane x+2y-3z=1.…

A: A set W is defined as consisting of all the planes in R3 that are parallel to the plane x+2y-3z=1.…

Q: Ametric space (x,d) is complete if and only ifx has the cantor intersection property

A:

Q: U = {a,b,c,d,e,f,g,h,i,o,u} A = {a,e,i,o,u} B = {a,c,h,e} C = {b,e,g,i} Find B’ Find (A U C)’…

A: The Universal set U is defined as U = {a,b,c,d,e,f,g,h,i,o,u} The set A is defined as A =…

Q: Theorem 23. If u, v E Q then we can find integers a, b, d with d > 0 such that u = a and v = d'…

A: By Division Algorithm we know that,               Let a, b be two integers with b&gt;0. Then there…

Q: Theorem: If R is a fuzzy relation on the set X, then (R-1)-1 = R

A:

Q: Let U​ =​{1, 2, 3, 4, a, b, c, d, e​}, E​ =​{1, 3, 4, c, d, e​},F​ =​{1, 2, b, c​}, and G​ =​{1, 2,…

A:

Q: Verify that {uq.u2} is an orthogonal set, and then find the orthogonal projection of y onto…

A:

Q: 3- A discrete topological space (X,T) is: a-To-space, b-T₁-space, c- T₂-space, d- No one.

A:

Q: 5)Let w-f(u, v), where u = X -y andv = a) Using the chain rule, express x-y in terms of x, y, of and…

A:

Q: 3. Let A, B, and C be three distinct collinear points such that AC <AB and BC < JAB. Prove that…

A: Let given points be in order A-B-C. But then AC can never be less than or equals to half of AB.…

Q: Let T={X, {a}, {a,b).{a,c,d}, {a,b,c,d}, {a,b,c}} be a topology on X=(a,b,c,d,e). (ii) Find N.…

A: Given : (X, T) be a topological space,  where  X = {a, b, c, d, e} and T = {X, ϕ, {a}, {a, b}, {a,…

Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: (R,t) usuall top space and A=(0,1),B = (a,b); a<b. prove A=~B ??

A:

Q: O Let ( X, T) be topdogical space and A,B CX- ldentify the Condition when a (Int(A)u FrlB) Ul F CA)…

A:

Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

Q: Prove that if A and B are sets, then (A∩B)∪(A∩B^' )=A

A: To prove : A∩B∪A∩B'=A   Let x∈A∩B∪A∩B' ⇒x∈A∩B or x∈A∩B' ⇒x∈A and x∈Bor x∈A and x∈B' In either of the…

Q: Let (X, T) be a topological space, AcX, then A'next (A) = 10 AO

A:

Q: Which of the following points is closest to (1,0, 1,0, 1, 1) using Hamming distance? O (1,1,1,1,1,0)…

A:

Q: ~ on T by (x1, y1, Z1) Let T 3D {(x, у, г) € R'| (х, у, 2) # (0, 0, 0)}. Define ~ on T by (х1, У1,…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

Q: B\ If X is Pre-Hilbert space then (x,ŻB,Y, ) = ΣP, (x,y, (x, j=1 j=1

A:

Q: Let A, B, C be subsets of X. show that Av (Bnc) - (AUB)n (AUC) AnCBUC) = (ANB)~ (ANC)

A:

Q: let A be a set. A:=(a1,a2,a3) in R^3 such that a1 is greater than 0 but less than and equals to 1,…

A:

Q: span (EE-EE) 3 O 2 O (A) and (B) O (A) ... = span Neither (A) nor (B). (B)... = span (4-6-8) 2 3 2 5…

A: Given that, span121, 031, 004, 152 We have to find the equivalent spanning set.

Q: 4 (6) Let U = {a, b, c, d, e, f, g, h } A = {a, f, h } B = {b, c, d, f } C = {b, c, d, e, g } %3D…

A: Given U = a, b, c, d, e, f, g, hA = a, f, hB = b, c, d, fC = b, c, d, e, g

Q: 3) if Aza,i + a₂j + a³k , 13 = bi + bj + bk Prove that the .(A-B) -13 -(DXA) - A - (DXB) Vactors

A: We have to show Note: In the question  is given which is incorrect. It should be

Q: Q1) Choose the correct answer 1- Let X be a non-empty set and r = (-0,a)| a €R) URU(0) then r is…

A: *Kindly keep a note in step 1️⃣ stating that as per our guidelines we are supposed to answer…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.