Sets
Sets
- A set is a collection of elements. Key notation:
- $n(A)$ = number of elements; $x \in A$ = $x$ is in $A$;
- $\mathscr{E}$ = universal set; $A'$ = complement (not in $A$); $\varnothing$ = empty set;
- $A \cup B$ = union (in either); $A \cap B$ = intersection (in both).
Practice
The symbol ∪ means:
∪ is union (in A or B or both); ∩ is intersection (in both).
Venn diagrams
- Draw each set as a circle inside the universal-set rectangle.
- Example: $A = \{2,4,6,8,10\}$, $B = \{3,6,9\}$ → $A \cap B = \{6\}$, $A \cup B = \{2,3,4,6,8,9,10\}$, $n(A\cup B) = 7$.
Practice
A = {2,4,6,8,10} and B = {3,6,9}. How many elements are in A ∩ B?
Only 6 is in both sets, so A ∩ B = {6}, which has 1 element.
Practice
For the same A and B, how many elements are in A ∪ B?
A ∪ B = {2,3,4,6,8,9,10}, which has 7 elements.
You've got it
Key idea
- $\cup$ = union (either), $\cap$ = intersection (both), $A'$ = complement
- a Venn diagram shows sets as overlapping circles
- $n(A)$ counts the elements of $A$