Unit 2: Sets, Logic,
Probability
2.1 Introduction to Sets/Venn Diagrams
- A set is a collection of elements that all share a property.
- Sets are always labeled with capital letters.
- Elements exist within sets and always take lower case letters.
means ‘the union
of set A and set B’. If an element belongs to either set A or set B or
both, then it belongs in the union.
means ‘the intersection of set A and set B’. If an element belongs to set
A and set B at the same time, it belongs to the intersection.
means ‘x is an element of A’
means ‘set A is a subset
of set B’. It means the whole of
set A exists within set B.
refers to the
number of elements in set A
or 
both indicate disjoint sets. Disjoint sets have no elements in
common.- U is reserved for the Universal Set. U always contains all elements relevant to the context of the question.
refers to the compliment
of set A. contains all elements that are not in set A.- Sets can be finite or infinite. This refers to the number of elements in the set. If you can count the number of elements, the set is finite.
- Set
builder notation:
reads ‘the set of
all x such that x is an integer between -2 and 4,
inclusive’.
Venn Diagrams are used to graphically display the interactions between sets. Circles are used to represent the sets, with a box around it to represent the universal set.
Ex 1
and
. Draw a Venn Diagram.
Ex 2
. Draw a Venn Diagram.
Ex 3
,
,
. Draw a Venn Diagram. Identify
.
Ex 4
,
,
. Draw a Venn Diagram. Use
terminology to describe the relationship between A and B.
Ex 5 A platform diving squad of 25 has 18 members who dive from 10 m and 7 who dive from 4 m. How many dive from both platforms? Draw a Venn Diagram to illustrate this.
Principle of Inclusion/Exclusion
p.69#1-5
p.77#1-4
p.80#9-12