How many one-to-one functions are there from a set with two elements to a set with two elements?

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How many one-to-one functions are there from a set with two elements to a set with two elements?

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Answer:TwoStep-by-step explanation:We are given that two sets  and each set have two elements.We have to find how many one- one function are formed from a set of two elements to a set with two elements.Let A={a,b}B={1,2}One-to-One function:If a function is one-to-one then different elements of set A is mapped with different elements of set B.Two elements of set A have not same image.If an element 'a' of set A is mapped with an element '1' of set B.Then , element b of set A is mapped with element '2' of set B.If an element 'a' of set A is mapped with element '2' of set B.Then, only one choice for element b and it mapped with element '1' of set B.Therefore, there are two possible cases and  two one-to-one function are formed from  a set of two elements to a set of two elements.Hence,two one-to- one functions are formed from a set with two elements to a set with two elements

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