The Power Set a) Let A = {a, b, c}. Find P(A). b) Let B = {0, 1} Let f: P(A) → B. The input of f is a subset of A. Define the output of f as S1 if ber f(x): l0 if b x Draw a map diagram of f. Use the diagram to justify that f is a function.

Q: Let A, B, C denote sets. Let g, h : A → B and f : B → C denote functions. Assume f is one-to-one and…

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Q: Let  X = {a, b, c}  and  Y = {d, e, f, g}.   Define functions H and K by the arrow diagrams below.…

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Q: Consider a ruler that takes as input any integer z and outputs. Is r a function? Why?

A: Given that r takes input as integer z and outputs Here the input is different while the output is…

Q: Let f, g be two functions from a set A to itself. If f o g is surjective, does it imply that g o f…

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Q: b) Let the set A = {-1,0, 1} and consider the following function: f2 A → A given by f₂(x) = (-x)4.…

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Q: Let A = {10, 11, 12, 13}. Let f: A Rbe a function defined below. Which of the following functions is…

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Q: d) Let the set A = {1, 2, 3,4} and let P(A) denote the power-set of A. Consider the following…

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Q: let a= {0,4,9,1.6} , b={0,3,6,12,20} and f a function. from a to b with f(x)=√x + x. A. Find f(0),…

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Q: Let f : A →B and g : B →C denote functions, and assume g ◦f is injective. a. Prove or disprove: The…

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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: Let Q: A - B be a function and CSA. define the restriction and also the extension of a function

A: Restriction and extension of a function

Q: Let A = {a, b, c, d} and f = { (a, 0), (c, 12), (d, 18), (b, 12) }. Is f a function from A to B ?…

A: Given, A = {a,b,c,d} f = {(a,0) , (c,12) , (d,18) , (b,12)}

Q: Refer to the functions f and g and evaluate the functions at x =-2. f = {(2, -1), (1, 1), (-4, -6),…

A: (f+g)(-2)=f(-2)+g(-2)  Substitute   f(-2)=-8  ,    g(-2)=-5in the above equation

Q: Use the graphs of f and g (see attached) to evaluate the composite function : (g ∘ f)(0)

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Q: Let A = {d, e, f} and B = {0, 1} Define a relation as follows: ARB = {(d, 1), (f,0)} Select the…

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Q: Let A = {2, 3, 4, 5} and B = {6, 8, 10}. A relation R is defined from A to B by a R b if a | b and…

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Q: Let R be a relation on Z given by aRb if and only if a = b². Is this relation a function? Justify…

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Q: Use two of the following sets for each part below. Let X = {a,b,c}, Y = {1, 2, 3, 4} and Z = {s, t,…

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Q: Let f: A → B be a function, and let C be any set such that BCC. True or False: f : A → C is always a…

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