Sets and Elements
These QuickNotes give you the most important points to remember for the ESSLCE. They are based on the MoE Grade 9 Mathematics Textbook, Unit 1, Chapter 1.1.
~3 min read- A set is a group of well-defined objects called elements.
- “Well-defined” means you can always tell if an object is in the set or not.
- We write a ∈ A if a is in set A, and b ∉ A if b is not in set A.
- Sets use capital letters (A, B, C); elements use small letters (a, b, c).
Key Words
- A set is a collection of well-defined objects.
- An element is one object that belongs to a set.
- Well-defined means there is a clear rule to decide if an object is in the set.
- The symbol ∈ means “is an element of” (belongs to).
- The symbol ∉ means “is not an element of”.
Picture it
a is inside A, so a ∈ A. b is outside A, so b ∉ A.
What a Set Is
- A set is a group of well-defined objects. Each object in the set is called an element.
- A set is well-defined when you can always decide if an object is in it or not. “The set of even numbers less than 20” is well-defined, but “the set of kind students” is not, because people may not agree on who is kind.
- We write set names with capital letters like A, B, C, and we write elements with small letters like a, b, c.
Belongs To (∈) and Does Not Belong To (∉)
- If a is in set A, we write a ∈ A and say “a belongs to A”.
- If b is not in set A, we write b ∉ A and say “b does not belong to A”.
- For example, if A is the set of vowels, then a ∈ A and o ∈ A, but b ∉ A.
Common Mistakes to Avoid
- A group is a set only if it is well-defined. “Tall students” or “kind people” are not sets, because there is no clear rule.
- The symbol ∈ is for one element, not for a whole set.
Easy Ways to Remember
- The symbol ∈ looks like the letter “e” for “element”. If x is an element of A, write x ∈ A.
- Capital letters name the set; small letters name the elements inside it.
Quiz
Tap an answer to check it.
1. Which one of the following is a well-defined set?
We can always decide if a number is even and less than 20. The others depend on opinion.
2. Let A be the set of positive even numbers. Which statement is true?
4 is a positive even number, so 4 ∈ A. 5 is odd, and 0 and -2 are not positive.
3. Which collection is NOT a well-defined set?
People may not agree on who is kind, so there is no clear rule. That makes it not well-defined.
Remember: A set is a group of well-defined elements. Use ∈ when an element belongs to the set, and ∉ when it does not.