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Q: Let (X,T) be a toplogical space, A, BC X. Show that АС В Ас в, АсВ. 介

A:

Q: Show that |qbu)|&x + 7元? the closed on interval [-元,T」 fo1 -π2 2くだ gluen that glven gux) for

A: Given g (x) = x +x² To find the maximum value of g(x). We can differentiate the function and equate…

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

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

Q: Verify that He follow egunbin is an ielartiky Fan o -sino 2 tano

A: We will use various trigonometric formulas to answer this

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…

A:

Q: Determine whether is a linearly independent set of vec- 3 11 tors in R3.

A: A set of vectors v1,v2,v3,…,vk in a vector space is said to be linearly independent if…

Q: 2. Determine whether the following multigraphs are Eulerian, semi-Eulerian or neither. Explain your…

A: Explanation we have to shown whether the given multigraphs are Eulerian , semi-Eulerian or neither…

Q: Let X and Y be two T, spaces, then X×Y. :is

A:

Q: 4).ェ Pare subset, -f y such that CeD than fic) is not eD, then the Convers %3D そイue.

A: Solution As it's mention C=D and f^-1 same , so each and every element from  f inverse we get equal.…

Q: Use the Ruler axiom to prove that there is a one-to-one correspondence between any two lines.

A:

Q: Let A=span(u,v) and B=span(u,v,w). Which statement is true? - A ≠ B and that is all you can say…

A: Let A=span(u,v) and B=span(u,v,w).

Q: E is closed. - E is complete, i.

A: It is given that X is a complete metric space and E is a subset of X. We have to prove that the…

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: Please solve 4,5,6,7 The Borel o-algebra on Ris generated by any of the following collections of…

A: As per the company policy, in a multipart question like this, we can solve only the first two…

Q: Suppose metric space X is not path-wise connected then X is not connected. O True O False

A: Question 9 Answer: as a path connected space of employees connected but converse is not true. So I…

Q: Dyani wrote a proof to show that ZXWY ZYZX. What is her error? Since ZWXZ LZYW, LXZW LYWZ, and XW…

A:

Q: Q: In usual topological space (R.Tu). answer the following: 1- Is [0,1] is compact set in R? Why?…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

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: let (X, Z) %3. üit piece wise comnected ?

A:

Q: Classify the discontinuity of as a removable, jump or infinite?

A: This question is related to continuity and differentiability.

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: which axioms for a finite projective plane are also valid in Euclidean geometry? which are not?

A: A finite geometry is any geometric system that has only a finite number of points. The familiar…

Q: An operation * is defined on the set R by x * y = x +y+ 6 where x, y are elements of R. What is…

A:

Q: The intersection of sets K and L will

A: our objective is to find the intersection

Q: Prove that interval [0,1] is uncountable.

A:

Q: Let A, B, C be points in 3-space. Suppose that AB represents u and BC represents v. Then AC…

A: Given statement is true.   Because it is following triangle rule of vector addition.   According to…

Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: ☺ Let (u,Ue...,un) be a lineorly ndependent list. Which True Statement? is a has --- a non-zero…

A:

Q: Use the definition to prove that {(-

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Q: If x<y, prove that x<(x+y)/2<y?

A:

Q: show that d connot be obtained from a norm.

A:

Q: Show that K, is not planar.

A: To prove: K5 is not a planar graph. Proof:  This is proved by the method of contradiction. We use…

Q: #3) Determine whether the funchon 2XZ72 iS onto if; @ flmin)= mtn © f(mm) =m-D O f(m, n) = Ini @…

A: Option (a) and (c) are correct. In both these cases, if we fix n=0 then by changing the value of m…

Q: 3. If u= (x+y +z') , prove that +y

A:

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Show that the interval [0,1] is a closed set in R

A:

Q: Solve the BVP on interval Lo, nJ) 2 %3D 2.

A:

Q: جليلة Let I = [= 1,₂1] ISR interval w that I is negligible Set.

A:

Q: prove with a table if x → y then xor y xor y = y

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Give all boundary points of D.  Is D open, closed or bounded? Justify all your answers.

A:

Q: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

A:

Q: Show that if ƒ′′&gt; 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

A: Given:

Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

Q: Show That R is Banach Sface.

A: To Show -

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d), {b,c,d,e}), therm %3D O (X,T) is…

A:

Q: The segment addition postulate can't be proven using a two column proof. O True O False

A:

Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.