Let π D₁ = {z € C\{0} : < Arg z < 4 D₂ = {z € C: 0 ≤ Re(2) ≤ ½ & 0 ≤ Im(2) ≤ 1}. a) Sketch D₁ and D₂ on separate Argand diagrams and for each set state whether it is a domain. Explain your answer. b) Find and sketch the image of D₁ under the mapping w = 1. c) Find and sketch the image of D₂ under the mapping w = ¹². eiz

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Q: Let A = {1, 2, 3, 4, 5}. Define the following relations on A. R1 = {(1,1), (1,2), (2,1), (3,2),…

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Q: Q3: Let A = {a, b, c, d} and define relations Ri. R, Rs, and Ri on A, what would be their directed…

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Q: Find a set A and a relation R such that the relation is symmetric, and not reflexive and transitive.

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Q: Let A = {3,4,5,6} and B = {1,2,3} and define a relation R: A → B as follows: For all (x, y) ∈ A × B,…

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Q: 4x² + y² Consider the function f(x, y) : 2

A: Consider the function fx, y=4x2+y22. i) Draw a cantour map of f for k=0, 1, 2, 3. ii) Using the part…

Q: A = Z*; a R b if and only if |a – b| < 2.

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Q: Direction: Define subsets of Za, as follows: A = {a | a E Za and a 5} A = {a | a E Za and 3| a} 1.…

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Q: i. Which of the following relations ƒ: Q → Q define a mapping? In each case, supply a reason why f…

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Q: A = {1, 3} and B = {2, 4, 6}. Define a relation R from A to B as follows: for all (x, y) ∈ A × B…

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Q: r1 1 1 0- 1 0 0 c) The matrix M represents the relations R defined. = 1 1 11 the set A = {1, 2, 3,…

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Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

Q: a. Let A= {0,1,2,3} and define a relation R on A as follows: R= {(0, 2), (0, 3), (2, 0), (2, 1)}. i.…

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Q: 3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

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Q: c) Find the characteristic polynomial of each of the restricted maps Tw and Tu. d) Determine whether…

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Q: Let A = { -1, 0, l}. Find mappings f: A -------------- A and g: A --------- A such that f o g ≠ g o…

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Q: 4), (4,2)} Draw the diagraph of R

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Q: b) The relation R on A = {a, b, c, d} is defined by the following digraph. b (i) List all paths of…

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Q: Let S = {1,2,3,... 18} and define the relation R by xRy if xly. Draw the Hasse diagram for R.

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Q: Find the rank of the mapping h : P4 → P4 defined by h(a + bx + cæ² + dæ³ + ex*) = 2c + 6dx + 24ex²

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Q: Exercise 4.4.5. Let A and B be sets. Prove that there is a bijective function f: A × B → BXA.

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Q: Consider the mapping diagram below. a 3 4 a) Write f as a set of ordered pairs. b) Is f 1-1? Justify…

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Q: X 1+x² List the elements of the requested image or preimage. No set notation needed. Let q be the…

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Q: Let T be the relation in the set of real numbers IR defined by xTy of both xe [n, n+1] and ye[nin+1]…

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Q: Consider the mapping diagram of the relation R below. 2. 3 a) State a counterexample from the…

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Q: Let R = {(0, 0), (1, 1), (-1, -1)} be a relation on set A. Deduce the rule between x and y for order…

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