Sets, Relations and Functions

Name: Sets, Relations and Functions
Author: StemPy Lab

How many students in a class like neither tea nor coffee, when you know how many like each, and how many like both? Sets answer this kind of question. In this course we learn the language of sets, we pair the elements of two sets in relations, and we find the special relation that we call a function, with its domain and its range.

3 lessons, about 1 h 25 min3 simulations11 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Sets and their operations
A set is a collection in which it is clear what belongs. We write sets in roster form or in set-builder form, and we meet subsets, the empty set, intervals, union, intersection, difference and complement. For two finite sets, $n(A \cup B) = n(A) + n(B) - n(A \cap B)$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 2about 25 min
Ordered pairs, products and relations
An ordered pair (a, b) has a first and a second element, and the order matters. The Cartesian product A × B is the set of all ordered pairs, with $n(A \times B) = n(A)\,n(B)$ . A relation from A to B is any subset of A × B. Its domain is the set of first elements, and its range is the set of second elements.
1 simulation2 practice questions1 Python program3 problems
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Lesson 3about 30 min
Functions, domain and range
A function from A to B is a relation in which every element of A has exactly one image in B. A is the domain, B is the codomain and the set of images is the range. A graph is the graph of a function if no vertical line meets it twice. We find the domain of a formula by ruling out division by zero and the square root of a negative number.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set1 note
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Sets, Relations and Functions: Practice Paper

15 questions · 20 min

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Sets, Relations and Functions

Course outline (3 lessons)

Sets and their operations

Ordered pairs, products and relations

Functions, domain and range

Test Your Learning

Your teacher

Discussion (0)