In each part of this question, you are asked to give an example of something, and explain why it is an example. You may use all definitions, lemmas, theorems etc. from the lecture notes. (a) A set ECR with exactly two limit points.

Q: Show that S CR is a closed set if and only if S contains all of its limit points.

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Q: lim 1+ 3x = -5 X--2

A: To prove: limx→-21+3x=-5 Solution: Given, limx→-21+3x Here function f(x)=1+3x is a linear function…

Q: f) Is the relation R, defined on the set of real numbers by xRy if 2x + y = 3. antisymmetric? g) Is…

A: Use the definition of antisymmetric to check whether the given relation is antisymmetric or not.…

Q: Can anyone please explain what limits are? And why limits are used?

A: The detailed explanation of limits is  given below in next step

Q: let à = (3,4,5) and To (5,2, 6) a Find (2-6) x (a+b)

A: We need to find out the cross product.

Q: 1. Let X be the set of real numbers with the usual pseudometric. Find the derived set and the…

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Q: (1) Write the definition of a measurable set ECR. (2) By writing the definition of the measurability…

A: Let m* be the outer measure of the power set of the set ℝ. A subset E⊂ℝ is said to be measurable if…

Q: Which of the following sets spans IR³? O ((0,1,-1),(0,0,0) O {(-3,0,2).,(5,1,0),(0,1,-1)} {(0,1,-1)}…

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Q: QUESTION 6 Let F(x,y): "x is friend with y", N(x). "x is funny", W(x): "x is wise", R(x): "x is…

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Q: Does the Sandwich Theorem also holds for limits?

A: The Sandwich Theorem states that, for all numbers x, if the functions f, g and h are related as…

Q: (1++*+) ... 2 22 2k

A: Given below the detailed solution

Q: Question 1 Let A = (-2,4), and B = 0, ox). Choose sets that are infinite and uncountable. O B\A B nQ…

A: Use the properties of set and countable sets to solve this problem.

Q: Use a graph to estimate the values of x such that  ex . 1,000,000,000.

A: ex=1,000,000,000

Q: QUESTION 3 Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is…

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Q: Compute the following limit folowing if they exist. lim .3 z² + 4 .2

A: We have to first check the tending values of numerator and denominator.

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

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Q: (2) Give an example of a universal set U and a set A so that U is infinite and A is infinite and A…

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Q: Which of the following sets spans R³? None of these O {(0,1,-1)} O {(0,1,-1),(0,0,0)} O…

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Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

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Q: 3. Select all that are true. 1600 1500 1400- 1300 1200- 1100 1000 900- 10 Distance Hiker Travels…

A: Domain is defined as the set of values of x for which the function is defined. Range is the set of…

Q: The set of circles centred at the point (-2, 3). More generally, given a fixed point (a, b), what is…

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Q: Give the 12 limit theorems by words.

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Q: How to prove the following: if A ⊂ image f then f(f -1(A)) = A.

A: The details are given in step 2.

Q: 10. Let A = (1, 2, 3, 4, 5). Which of the following sets are equal to A? (a) (4, 1, 2, 3, 5} (b) {2,…

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