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

A: ex=1,000,000,000

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: 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: 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: 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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