 # Set of a which is the set of all subsets of a

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set of A which is the set of all subsets of A.
(f)Let A be defined to be the set {1, 2, 3, 4, 5, 6, 7, 8}. f: P(A)P(A). For X ⊆A, f(X) = X. Recall that for a finite set A, P(A) denotes the power set of A which isthe set of all subsets of A.SolutionOne-to-one and onto.(g)Let A be defined to be the set {1, 2, 3, 4, 5, 6, 7, 8} and let B = {1}. f: P(A)P(A). ForX ⊆ A, f(X) = X - B. Recall that for a finite set A, P(A) denotes the powerset of A which is the set of all subsets of A.
4.4.1: Arrow diagrams for inverses of functionsEach of the arrow diagrams below define a function f. For each arrow diagram,indicate whether f-1is well-defined. If f-1is not well-defined, indicate why. If f-1iswell-defined, give an arrow diagram showing f-1.(a)
(b)
Solutionf-1is well-defined.(c)
4.4.2: Finding inverses of functionsFor each of the following functions, indicate whether the function has a well-defined inverse. If the inverse is well-defined, give the input/output relationshipof f-1.(a)f:ZZ. f(x) = x + 3
(b)f:ZZ. f(x) = 2x + 3
(c)f:RR. f(x) = 2x + 3
Let A be defined to be the set {1, 2, 3, 4, 5, 6, 7, 8}. f: P(A){0, 1, 2, 3, 4, 5, 6,7, 8}. ForX ⊆ A, f(X) = |X|. Recall that for a finite set A, P(A) denotes the powerset of A which is the set of all subsets of A.
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Term
Spring
Professor
Meenakshisundaram
Tags
Finite set, Bijection
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