IGCSEMathsEdexcelMaths BFlashcardsSetsSet Notation & Venn Diagrams

Set Notation & Venn Diagrams (Edexcel IGCSE Maths B): Flashcards

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FrontSet Notation & Venn Diagrams
Define a set, and state how its elements are written down.

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Define a set, and state how its elements are written down.
A set is a collection of elements, which can be numbers, letters, coordinates or anything else.
Its elements are listed inside curly brackets, so the set of factors of 6 is $\{1, 2, 3, 6\}$ .
Sets are named with upper case letters and their elements with lower case letters.
The set $\{x : x^{2} < 30\}$ can have a type of element, such as "positive integer", written before the colon. What do the two parts either side of the colon tell you, and which positive integers does the set contain?
The part before the colon gives the type of element, and the part after it gives the rule those elements must follow; the colon is read as 'such that'.
So this is the set of positive integers whose square is less than 30, which is $\{1, 2, 3, 4, 5\}$ .
A vertical bar is sometimes used in place of the colon.
True or False?
$\{x : x^{2} < 30\}$ contains only the positive integers whose square is less than 30.
False.
When no type is given before the colon, $x$ may take any value at all.
So negative numbers, fractions and irrational numbers count too: $- 4$ , $2.5$ and $\sqrt{7}$ all belong to this set.
Define the universal set, and state the symbol used for it.
The universal set is the set of everything being considered in a particular problem, and it is written $E$ .
For example, if only the factors of 24 are of interest, then $E = \{1, 2, 3, 4, 6, 8, 12, 24\}$ .
You may also meet $U$ , $S$ or $ξ$ used for the universal set, none of which is the union symbol $\cup$ .
If $A = \{1, 4, 9\}$ , what is $n (A)$ , and what does that notation mean?
$n (A)$ means the number of elements in set $A$ .
Set $A$ has three elements, so $n (A) = 3$ .
Fill in the two missing set symbols.
$3______\{1, 2, 3\} but 4______\{1, 2, 3\}$
The completed statement is:
$3 \in \{1, 2, 3\} but 4 \notin \{1, 2, 3\}$
$\in$ means 'is an element of', and $\notin$ means 'is not an element of'.
$A = \{5, 6, 7, 8\}$ and $B = \{3, 7, 11\}$ . Write down $A \cap B$ and $A \cup B$ .
$A \cap B$ is the intersection, the elements that are in both sets, so $A \cap B = \{7\}$ .
$A \cup B$ is the union, the elements that are in at least one of the sets, so $A \cup B = \{3, 5, 6, 7, 8, 11\}$ .
Define a subset, and state the symbol used for it.
Set $A$ is a subset of set $B$ if every element of $A$ is also an element of $B$ , written $A \subset B$ .
For example $\{1, 2, 3\} \subset \{0, 1, 2, 3, 4\}$ , while $A ⊄ B$ says that $A$ is not a subset of $B$ .
If $E = \{1, 2, 3, 4, 5\}$ and $A = \{1, 3\}$ , write down $A'$ and say what the notation means.
$A'$ is the complement of $A$ : every element of the universal set that is not in $A$ .
So $A' = \{2, 4, 5\}$ .
On a Venn diagram, what do the rectangle and the circles represent?
The rectangle represents the universal set $E$ , and each circle inside it represents one set.
Circles are drawn overlapping where the sets share elements, so two sets with no elements in common are drawn as circles that do not overlap.
For two sets $A$ and $B$ drawn on a Venn diagram, a student claims that $A' \cap B' = \emptyset$ . What is the student claiming?
$\emptyset$ is the empty set, also called the null set, which contains no elements at all.
So the claim is that nothing lies outside both circles: every element of $E$ is in $A$ , in $B$ , or in both.
The claim is wrong as soon as there is anything in the region outside both circles.

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