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: Let f: R →R be defined as Sr + 2, if a < 1, 1-2a, if a 21. S(1) Plot f(r) of f of all r) Based on…

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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: Let A = {8,9, 10, 11}. Let f : A R be a function defined below. Which of the following functions is…

A: Given A= {8, 9,10,11} Function the one to one function?

Q: Let A = {a, b, c}. Define the function f: p(A)→N, by f(X) = card(X), where p(A) be the power set of…

A: Given A = {1,2,3} then ρ(A) = {ϕ , {a} , {b} , {c} , {a,b} , {a,c} , {b,c} , {a,b,c}} Define f :…

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 = B = {a, b, c, d}. The function f is defined from A to B which is given below: f = {(a, a),…

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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: Given the relations F = {(q, p)|5p − 4q2 − 3 = 0 p, q ∈ ℝ} and                                G =…

A: Given relations are  F=q,p:5p-4q2-3=0 , p,q∈ℝ        (i)F=p,q:5p-4q2-3=0 , p,q∈ℝ        (ii) Let,…

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: 8. Let A = {1,2} and B = {a, b, c}. For each of the following cases, decide whether the set…

A: The set A={1,2}, B=a,b,c &amp; f:A→B. a) 1,a,2,b b) 1,b,2,b c) 1,a,1,b,2,c

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

A: Here given  A=-1, 0, 1 Now consider two functions as f:A→Afx=1g:A→Agx=0

Q: Let G be a relation from C={-1, 0, 1, 2} to C {-2,-1, 0, 1, 2} with G={(-1,0), (0,1),(1,2), (2,-1)}.…

A: Given query is to find G is a function or not.

Q: Let f:R R be a function given by f(x)=x+1. The value of f[10,37]will be: Pick ONE option [3,6]…

A: Given function is: fx=x2+1 f3=32+1=9+1=10f-3=-32+1=9+1=10f6=62+1=36+1=37f-6=-62+36+1=37

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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Q: Consider the function G below: G Select all statements below that are true: Rng(G) = (a, b, c, d, e)…

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