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jy02354441
- 2
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how to prove it please?
An injection is a function that maps each element of its domain to a unique element in its codomain. In other words, each input has only one corresponding output.
The composition of two injections is the function resulting from applying one injection to the output of the other. This means that the composition of injections is also an injection.
To prove that the composition of injections is an injection, we need to show that for any two injections f and g, the composition f(g(x)) is also an injection. This can be done by showing that for any inputs x and y, if f(g(x)) = f(g(y)), then x = y.
The notation for an injection is f: A → B, where A is the domain and B is the codomain. This can also be written as f(x) = y, where x and y are elements of A and B, respectively.
Proving that the composition of injections is an injection is important because it ensures that the resulting function is one-to-one, meaning that each input has a unique output. This property is useful in various areas of mathematics and computer science, such as cryptography and data compression.