Study Notes
Set language involves understanding sets as collections of distinct objects and using various notations to represent them. Absolute value refers to the non-negative value of a number, representing its distance from zero on a number line.
- Set — a collection of distinct objects. Example: A = {1, 2, 3, 4, 5}
- Element — an object within a set. Example: 12 ∈ A
- Number of Elements (n(A)) — the count of elements in a set. Example: n(A) = 6 for A = {3,6,9,12,15,18}
- Complement of a Set (A′) — elements not in the set. Example: A′ = {Boys in the class} if A = {Girls in the class}
- Empty Set (∅) — a set with no elements. Example: A = ∅ for positive numbers less than zero
- Universal Set (U) — a set containing all elements of other sets. Example: U = {0, 1, 2, 3, 4, 5, 6} for sets A, B, and C
- Absolute Value — the non-negative value of a number. Example: |−5| = 5
Exam Tips
Key Definitions to Remember
- A set is a collection of distinct objects.
- An element is an object within a set.
- The absolute value of a number is its distance from zero.
Common Confusions
- Confusing the complement of a set with the set itself.
- Misunderstanding the notation for elements (∈) and non-elements (∉).
Typical Exam Questions
- What is the complement of set A if A = {1, 2, 3} and U = {1, 2, 3, 4, 5}? A′ = {4, 5}
- How many elements are in the set B = {x | x is a prime number less than 10}? n(B) = 4
- What is the absolute value of −7? |−7| = 7
What Examiners Usually Test
- Understanding and using set notation correctly
- Calculating the number of elements in a set
- Applying the concept of absolute value in different contexts