Onto, and one-to-one functions Function on power sets Let the set A = {1, 2, 3,...

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Onto, and one-to-one functions Function on power sets Let the set A = {1, 2, 3, 4, 5,..., 10} Let's define the function g on the power set of A, P(A) as follows: g: P(A) → Z defined by g(x) = 1 if X is even if X is odd 1. Calculate g({0}), g({1, 2, 3}), and g({1,2,3,4}). 2. Prove that g is not onto. 3. Prove that g is not one-to-one. 4. Propose a change in the co-domain of g to make the function onto. Onto, and one-to-one functions Function on power sets Let the set A = {1, 2, 3, 4, 5,..., 10} Let's define the function g on the power set of A, P(A) as follows: g: P(A) → Z defined by g(x) = 1 if X is even if X is odd 1. Calculate g({0}), g({1, 2, 3}), and g({1,2,3,4}). 2. Prove that g is not onto. 3. Prove that g is not one-to-one. 4. Propose a change in the co-domain of g to make the function onto.

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PA denotes power set of A ie collection of all subsets of set A g ... View the full answer