All but two of the following statements are correct ways to express the fact that a function f is onto. Find the two that are incorrect. a. f is onto ⇔ every element in its co-domain is the image of some element in its domain. b. f is onto ⇔ every element in its domain has a corresponding image in its co-domain. c. f is onto ⇔ ∀ y ∈ Y , ∃ x ∈ X such that f ( x ) = y . d. f is onto ⇔ ∀ x ∈ X , ∃ x ∈ Y such that f ( x ) = y . e. f is onto ⇔ the range of f is the same as the co-domain of f .
All but two of the following statements are correct ways to express the fact that a function f is onto. Find the two that are incorrect. a. f is onto ⇔ every element in its co-domain is the image of some element in its domain. b. f is onto ⇔ every element in its domain has a corresponding image in its co-domain. c. f is onto ⇔ ∀ y ∈ Y , ∃ x ∈ X such that f ( x ) = y . d. f is onto ⇔ ∀ x ∈ X , ∃ x ∈ Y such that f ( x ) = y . e. f is onto ⇔ the range of f is the same as the co-domain of f .
Solution Summary: The author explains that the statements (b)and (d ) are incorrect.
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