For each Ollowing subsets of the plane, draw the set, state whether it is open, closed, or neither, and justify your answer in a word or two: 270 LIMITS AND OPEN SETS [12] a) {(x, y) : -1 < x < +1, y = 0}, c) {(r. v) : x + y' = 1}. b) {(x, y) : x and y are integers}, d) {(x, y) : x + y < 1}, %3D e) {(x, r') : x = 0 or y = 0}.

Q: a (1, 0, 1), b = (2, 1, −1) and c = (1, -1, 4). Calculate |ax (b+c)].

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Q: m) Linearize : -3x 天ェ_= around %31

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Q: Show that both ℝ and ℝ2 may be covered by countably many open balls.

A: The answer provided below has been developed in a clear step by step manner.

Q: 8. Which expression is the simplest form of V48 – 4V6

A: Simplest form: - When an expression is easiest to employ, it is in its simplest form. Given: - The…

Q: What does the Theorem of Pappus say?

A:

Q: danx fonthebougast Awiwnitean quakin yo bomx+ fthe Camve Le Secx 19-

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Q: Use z = a + bi and w = c + di to show that z + w =7 + W.

A: Consider a complex number z=a+bi Then, the complex conjugate of above complex number is given by:…

Q: Z

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Q: let a1 is (-3,2,6) a2 is (-9,-7,-2) and b is (-18,-27,-23). Is b in the span of of a1 and a2

A: The objective of this question is to determine whether the vector b is in the span of vectors a1 and…

Q: Show that (A\B)\CC A\C.

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Q: Sketch ri-qcose

A: Given ÷ r2=9cosθ Curve is shown below

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: To show that the group &lt;a, b | a^5 = b^2 = e, ba = a^2b&gt; is isomorphic to Z2, we need to…

Q: Indicate that  R and R2 may be covered by countably many open balls.

A: To show that ℝ and ℝ2 covered by countably many open balls.

Q: |- 4X

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Q: Show that is isomorphic to Z2.

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Q: Is (2,1)=(1,2)?

A: The objective is to determine whether 2,1=1,2.

Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: ,3), calculate the value of a it the

A: We have to find the value .

Q: 1 Ita Į = ab

A: The objective is to show that, 11111+a1111+b=ab

Q: What is the cartesian product of sets {1,3,4} and {2,9}?

A: 1, 3, 4  and 2, 9

Q: Define Conjugate transpose.

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Q: TRUE or FALSE: A\B = A when A and B are disjoint

A: Given statement ,A|B=A then A and B are disjoint

Q: Use the Conjugate Pairs Theorem

A: Given: Use the Conjugate Pairs Theorem

Q: What is the Cartesian Product of A = {1,2} and B = {a,b}? Find AxB.

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Q: Explain why the Theorem of Pappus is useful.

A: To Explain: Why the Theorem of Pappus is useful.

Q: State and Prove Pick’s Theorem.

A: Let P⊂ℝ2 be a polygon with all vertices on lattice points on the grid Z2. Let  I be the number of…

Q: draw (A∪B) ∩C’

A: Draw a venn diagram

Q: What is cross ?

A:

Q: What are all of the theorems used in a ferris wheel?

A: A Ferris wheel is a type of amusement attraction that consists of a revolving upright wheel with…

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: We have to show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

Q: A cinema can accomodate 200 customers. Let z denotes the numbers of the customers in cinema. What…

A: Introduction: It is given that the cinema can accommodate 200 customers. The random variable z…

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…