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The chapter focuses on the concept of functions in mathematics, encompassing various types of functions including injective, surjective, and bijective functions. It explains the fundamental characteristics of functions, such as their domain and co-domain, as well as the concepts of function composition and inverse functions. A detailed exploration of these topics aids in understanding their applications in discrete mathematics.
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Sections
References
ch24.pdfClass Notes
Memorization
What we have learnt
- A function is a specific ty...
- Functions can be classified...
- The composition of function...
Final Test
Revision Tests
What we have learnt
- A function is a specific type of relation wherein each element from the domain is associated with exactly one element from the co-domain.
- Functions can be classified into various categories based on their properties: injective (one-to-one), surjective (onto), and bijective (both one-to-one and onto).
- The composition of functions is defined only when the range of the first function is a subset of the domain of the second function, and it is not necessarily commutative.
Key Concepts
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Term: Function
Definition: A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.
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Term: Injective Function
Definition: A function is injective if distinct elements in the domain map to distinct elements in the co-domain.
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Term: Surjective Function
Definition: A function is surjective if every element of the co-domain is mapped to by at least one element from the domain.
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Term: Bijective Function
Definition: A function is bijective if it is both injective and surjective, meaning there is a one-to-one correspondence between elements of the domain and co-domain.
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Term: Composition of Functions
Definition: The composition of two functions is a function that applies one function to the result of another function.
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Term: Inverse Function
Definition: An inverse function reverses the mapping of the original function, and it exists only if the function is a bijection.