1.1.1 Set Theory Flashcards
What is an element in set theory?
A possible outcome of an experiment.
Example: In a coin flip, ‘heads’ and ‘tails’ are elements.
What is a set?
A collection of zero or more elements. Denoted with uppercase letters (e.g., A), with elements separated by commas:
A = {a, b, c} where a,b,c are A elements
What is a sample space?
The set of all possible outcomes of an experiment. It is usually denoted by S.
Example: For a coin flip, S = {heads, tails}.
What is an empty set?
A set containing zero elements, denoted by ∅ or {}.
Example: The set of negative numbers in a standard die roll is ∅.
What is a subset?
A set A is a subset of B if all elements of A are also in B. Denoted as:
A ⊆ B
Example: If A = {1, 2} and B = {1, 2, 3}, then A ⊆ B.
What is a union of sets?
The set of all elements that are in at least one of the sets. Denoted as:
A ∪ B
Example: If A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.
What is an intersection of sets?
The set of elements common to both sets. Denoted as:
A ∩ B
Example: If A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.
What is the difference of two sets?
The set of elements in A but not in B. Denoted as:
A - B
Ex: if F = {1,2,3} and G={3,4,5} then F-G ={1,2} and G-F = {4,5}
Example: If A = {1, 2, 3} and B = {2, 3}, then A - B = {1}.
What is the complement of a set?
The set of elements not in A, but in the sample space S. Denoted as A^c or A’.
Example: If A = {odd numbers on a die} = {1, 3, 5}, then A^c = {2, 4, 6}.
What does it mean for sets to be mutually exclusive (disjoint)?
They do not share any elements.
A ∩ B = ∅
Example: If A = {1, 2} and B = {3, 4}, then A and B are mutually exclusive.
what is a venn diagram?
A Venn diagram, also known as a set diagram, is a diagram showing the relationship between a finite number of sets. Venn diagrams are useful to illustrate probabilities and events.
what is an event?
An event is a subset of the sample space. In short, events and sets are interchangeable, where an event is typically described in words.
The following are examples of an event: “coin flip result is a heads” and “die roll result is an odd number.”
