Hey everyone, in this video, we're exploring various types of functions and their properties. Functions come in different types, each with its unique characteristics. For example, an injective, or one-to-one function, assigns different inputs to different outputs. On the other hand, a surjective, or onto function, assigns to every element of the output set some input. A function that is both injective and surjective is termed bijective.

In this session, we'll identify these types of functions, determining whether they are injective, surjective, or bijective. For instance, consider the function f from {1,2,3} to {A,B,C}. As we see no repeated outputs, it's clearly injective. Since each element in the codomain is an output, the function is also surjective, making it bijective.

Now, consider another function G from {1,2,3} to {A,B} defined by G(1) = A, G(2) = A, and G(3) = B. Since G(1) and G(2) both equal A, the function is not injective. However, since both A and B are outputs, it is surjective.

Lastly, let's look at a function H from {1,2,3} to {A,B,C,D} defined by H(1) = A, H(2) = B, and H(3) = C. The function is injective as no outputs are repeated, but it is not surjective as D in the codomain isn't an output of the function H.

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