NXN set on " (a,b)~ (c,d) -) a+d -b+c %3D define d as, equiualence relation? Shaw Is reation ""

Q: 3. Consider the Cauchy-Schwarz inequality. That is, for u, v E R": Use some reasoning, or do some…

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Q: • if Rit is a symmetrical relationship then R-1 is not symmetrical False O true نقطة واحدة • ifA =…

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Q: 2. A stock market trader buys 100 shares of stock A and 200 shares of stock B. Let X and Y be the…

A: Given :  From the problem statement we know that X={-2,-1,0,1,2}  and Y={x±1}

Q: A(n)................................... is the collection of all points in the plane such that the…

A: We know, A parabola is a collection of all the points in a plane such that the distance from each…

Q: 21. Let A and B be two on-empty bounded sets of positive embers and let С%3D {ху: х€ А and y € B}.…

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Q: If R; = { (a,b) asb},then this relation is: %3D Select one: O Reflexive, Symmetric, Transitive O…

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Q: Consider the following relation R on R: (2, y) € R if and only if Va - y E Q. What are the…

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Q: Prove the Cauchy-Schwarz Inequality, ∣u ∙ v∣ ≤ ∣ u∣∣  ∣ v ∣∣.

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Q: 6. Use Cauchy-Schwartz Inequality, Ju· v| < ||u|| |v||, to prove the Triangle Inequality: ||u+ v|| <…

A: To Determine: Use Cauchy-Schwartz inequalities,                                  u.v≤u  v To prove…

Q: 3. Let R be the relation from X = {1,2,3,5} to Y = {0,3,4,9} defined by Ry if and only if x? = y.…

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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: 5. Let S be a set of negative numbers. Prove the least upper bound of S cannot be positive.

A: To show that the least upper bound of a set of negative numbers cannot be positive.

Q: if f is derivable in [a, b] and f' (a) not equal to f' (b), then for each number k lying between f'…

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Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is 9 an…

A: Let (M,d) be a metric space and let S⊆M. A point a∈S is said to be an Interior Point of S if there…

Q: set of real numbe of R defined resp

A: Given: A and B are two subsets of ℝ such that A=12,1,2,4 and B=0,1∪1,2. We have to check that A is…

Q: Let A -N- (0}.Let R-((xy)EAXA: x divides y). Then R. relation. symmetric O reflexive O equivalence O

A: Recall: If relation R is equivalence if it is reflexive, symmetric and transitive.

Q: (4) Every T4-space is: (a) T2-space (b) T3-space (c) To-space (d) All of them.

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Q: (d) Consider the set [1, √5] C [-1, √10]. Explain f is not continuous by (i) connectedness, (ii)…

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Q: يثبت The Cauchy-Schwarz inequality states that (f, g)| ≤ ||f||||g|| for every f, g ¤ H.

A: Using the property of inner product

Q: (b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact that ||ax + by |…

A: Given that, Euclidean metric d on Rn is defined as d(x,y) = || x - y || for x, y in Rn Part(a): Let…

Q: b Let A be a continuous fuzzy quantity. If all the a-cuts of A are closed intervals then show that A…

A: In the question provided it is given that A is a continuous fuzzy quantity. The objective is to show…

Q: Describe the set S = { x : I 1/2x - 3 I &gt; 4} in terms of intervals.

A: S=x : 12x-3&gt;4

Q: graph the inequality on a coodinate plane x &gt; with line under it 2

A: To graph the given inequality x≥2.The equation x=2 has a graph that is a vertical line with all…

Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: poundedness and the closedness are not opological properties because * O Ris homeomorphic to ]-00,…

A: A property of a topological space is called a homeomorphic property if it remains invariant under…

Q: A(n)............ is the collection of all points in the plane the sum of whose distances from two…

A: It is given that,   A(n) ............ is the collection of all points in the plane the sum of…

Q: Lie: Prove that every finite set S of R" has no accumulation point.

A: We have to prove this given statement

Q: the book is "First Course on Fuzzy Theory and Applications"

A: Differentiation at fuzzy point.f'(A) of non-fuzzy function or fuzzy set A is defined as

Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: chow. that there ks no sset which har the set Q os its only. set of accumulation points

A: Before entering to the problem , first of all think about accumulation point. A point 'x' is said to…

Q: Consider the following relationships about A = {1,2, 3} a) R1 = {(1,2), (1, 3), (2, 1), (2, 2)} b)…

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Q: Q2: Let (R,7) be the usual topological space f: (R,r) (R,7) fx? +1 :x 21 st. Ar) =-x ;x<1 . Isf…

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Q: 3. Consider the Cauchy-Schwarz inequality. That is, for u, v € R": Use some reasoning, or do some…

A: We have to prove ∑i=1nuivi≤∑i=1nui2∑j=1nvi2 Since we know the Holder's inequality…

Q: (c) Suppose n = 5 and m = 4, determine the number of onto functions from A to B.

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Q: What is the Boundedness Theorem?

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Q: has

A: We have to choose the correct option from the given options according to the given information

Q: Which characteristic/s implies(y) that a set S of real numbers is closed? S has no accumulation…

A: To choose correct option from given question.

Q: Let S be a set of negative numbers. Prove the least upper bound of S cannot be positive.

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

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Q: be a set d differentioble fenetlans. Define Phe cxC by fSa A and XER on orly 'x) for all ve an…

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Q: 5. Differentiate with respect to x: SET A. 5e

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Q: Explain the Cauchy–Schwarz Inequality?

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

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Q: 1. For what values of k is the null space of A = k -1 a line?

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Q: Describe the set S = { x : I } x - 3 I &gt; 4} in terms of intervals.

A: S=x : x-3&gt;4 Now consider, x-3&gt;4⇒x-3&lt;-4  or  x-3&gt;4   ∵x&gt;a⇒x&lt;-a  or  x&gt;a⇒x&lt;-1…

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is F closed?

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Q: For every element x in A, there is an element in y is B such that (x,y)∈F. QUESTION: How does this…

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