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Mathematics · Class 10 · Chapter 17: Sets and Functions

8 min

Key points

Set is a well-defined collection of distinct objects called elements or members
Function is a special type of relation where each element in domain has exactly one image in codomain
Domain is the set of all first elements (x-values) of ordered pairs in a function
Range is the set of all second elements (y-values) that are actually used in a function
Codomain is the set from which the second elements of ordered pairs are taken
One-to-one function means no two different elements of domain have same image
Onto function means range equals codomain - every element of codomain is used
Bijective function is both one-to-one and onto function
Composite function (f∘g)(x) = f(g(x)) - apply g first, then f to the result

Definitions

Function: A function is a relation in which each element of the domain is paired with exactly one element of the codomain
Domain: The domain of a function is the set of all first components (x-values) of the ordered pairs
Range: The range of a function is the set of all second components (y-values) that are actually used
One-to-one Function: A function is called one-to-one if different elements of the domain have different images in the codomain
Onto Function: A function is called onto if every element of the codomain is the image of at least one element of the domain

Worked example

If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A ∪ B and A ∩ B. Also define union and intersection of sets. (6 marks)

Union of sets: The union of two sets A and B is the set of all elements which belong to A or B or both. A ∪ B = {1, 2, 3, 4, 5, 6}. Intersection of sets: The intersection of two sets A and B is the set of all elements which are common to both A and B. A ∩ B = {3, 4}

Common mistakes

Students confuse domain and range - remember domain is input (x-values), range is output (y-values)
In composite functions, students apply functions in wrong order - (f∘g)(x) means f(g(x)), apply g first
Students think all relations are functions - a function must pass vertical line test
Confusing range and codomain - range is subset of codomain
Not writing function notation properly - always write f(x) = instead of just y =

Quick recap

Sets are well-defined collections of objects. Functions are special relations where each element in domain maps to exactly one element in range. Union combines all elements, intersection finds common elements. Always write textbook definitions exactly as given in STBB for full marks.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.