Question
PLEASE TYPE ONLY*** THEORY FOUNDATION SUBJECT*** Exercise 3.3.4: Properties of functions on strings and power sets. For each of the functions below, indicate whether the
PLEASE TYPE ONLY***
THEORY FOUNDATION SUBJECT***
Exercise 3.3.4: Properties of functions on strings and power sets.
For each of the functions below, indicate whether the function is onto, one-to-one, neither or both. If the function is not onto or not one-to-one, give an example showing why.
(e)
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}. For X A, f(X) = |X|. Recall that for a finite set A, P(A) denotes the power 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) = A-X. Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A.
(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). For X A, f(X) = X - B. Recall that for a finite set A, P(A) denotes the power set of A which is the set of all subsets of A.
(h)
A = {a, b, c}, h: P(A) P(A). For X A, h(X) = X {a}.
(i)
A = {a, b, c}, h: P(A) P(A). For X A, h(X) = X {a}.
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