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A bijection function is both one-one and...

A bijection function is both one-one and onto?.

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To determine whether a bijective function is both one-one and onto, we can follow these steps: ### Step 1: Understand the Definitions - **Bijection**: A function is called a bijection if it is both one-one (injective) and onto (surjective). - **One-One (Injective)**: A function f: A → B is one-one if different elements in A map to different elements in B. In other words, if f(a1) = f(a2), then a1 must equal a2. - **Onto (Surjective)**: A function f: A → B is onto if every element in B is the image of at least one element in A. This means that the range of the function is equal to the codomain. ### Step 2: Analyze the Bijection Since a bijective function is defined as being both one-one and onto, we can conclude that: - If a function is bijective, it must satisfy both properties: - It must be one-one, meaning no two different elements in the domain map to the same element in the codomain. - It must be onto, meaning every element in the codomain is covered by the function. ### Step 3: Conclusion Thus, we can definitively say that a bijective function is indeed both one-one and onto. ### Final Answer Yes, a bijective function is both one-one and onto. ---
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