Important Formulas: Venn Diagrams & Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Set Theory

A set is a group of objects. Each object is known as a member of the set. A set can be represented using curly brackets. So a set containing the numbers 2, 4, 6, 8, 10, ... is: {2, 4, 6, 8, 10, ... } . Sets are often also represented by letters, so this set might be E = {2, 4, 6, 8, 10, ...} . Alternatively, E = {even numbers} .

Common Sets

Some sets are commonly used and so have special notation:

for example:

means that x is in the set of integers,
i.e x is a integer
ϵ means ' is a member of '

Other Notation

Subsets

• If A is a subset of B, then all of the elements of A are also in B. For example, if A = {1, 2, 3} and B = {1, 2, 3, 4, 5} then A Í B (Í means is a subset of).

Number of Members

• If A = {1, 2, 4, 8}, then n(A) = 4. This is because n(A) means the number of members in set A.

The Universal Set

• The universal set is the set of all sets. All sets are therefore subsets of the universal set.

Venn Diagrams

• Venn diagrams are used to represent sets. Here, the set A{1, 2, 4, 8} is shown using a circle. In Venn diagrams, sets are usually represented using circles. The universal set is the rectangle. The set A is a subset of the universal set and so it is within the rectangle.
  
• The complement of A, written A', contains all events in the sample space which are not members of A. A and A' together cover every possible eventuality.
  
• A ÈB means the union of sets A and B and contains all of the elements of both A and B. This can be represented on a Venn Diagram as follows:
• AÇB means the intersection of sets A and B. This contains all of the elements which are in both A and B. AÇB is shown on the Venn Diagram below:
  
• An important result connecting the number of members in sets and their unions and intersections is:
  n(A) + n(B) - n(AÇB) = n(AÈB)