Set Notation & Venn Diagrams

Front

What is set notation?

Back

Set notation is a mathematical language used to describe a collection of objects, called elements, which are grouped together as a set. It often uses curly braces, e.g., {1, 2, 3}.

Front

What does the symbol ∈ represent in set notation?

Back

The symbol ∈ means 'is an element of'. For example, if x ∈ A, it means x is an element of the set A.

Front

What is a Venn diagram?

Back

A Venn diagram is a visual representation of sets and their relationships. It uses overlapping circles to show how different sets intersect and relate to each other.

Front

How do you represent the union of two sets A and B?

Back

The union of two sets A and B is represented as A ∪ B, which includes all elements that are in A, in B, or in both.

Front

How do you represent the intersection of two sets A and B?

Back

The intersection of two sets A and B is represented as A ∩ B, which includes all elements that are common to both A and B.

Front

What is the complement of a set A?

Back

The complement of a set A, denoted as A', includes all elements not in A, relative to a universal set U.

Front

If a survey shows that 30 students like dogs and 20 like cats, how do you find the total number of students surveyed?

Back

To find the total number of students surveyed, you need to add the number of students who like dogs and cats, considering any overlap (students who like both).

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

How do you calculate P(not A)?

Back

P(not A) is calculated as 1 - P(A), where P(A) is the probability of event A occurring.

Front

In a Venn diagram, if set A has 10 elements and set B has 5 elements with 3 elements in both, how many elements are in A ∪ B?

Back

A ∪ B = |A| + |B| - |A ∩ B| = 10 + 5 - 3 = 12.