Sets, Relations and Functions — Chapter Summary

A set is a well

A set is a well-defined collection of distinct objects. For example, the set of natural numbers less than 5 is {1, 2, 3, 4}. Sets can be represented i

The Cartesian product of two sets

The Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. For example, if A = {1, 2} and

A relation from set A

A relation from set A to B is any subset of A × B. A function is a special relation where every element of A has exactly one image in B. For example,

Functions can be classified based on

Functions can be classified based on mapping: one-one (injective) if distinct inputs give distinct outputs; onto (surjective) if every element in codo

A function f(x) is even if

A function f(x) is even if f(−x) = f(x), e.g., f(x) = x². It is odd if f(−x) = −f(x), e.g., f(x) = x³. Even functions are symmetric about y-axis; odd