Origin Of Sets Flashcards
(19 cards)
What is the definition of a set?
A collection of various elements such as numbers, symbols, letters.
Sets are represented in curly brackets: {123456}
What does ‘E’signify in set theory?
It signifies ‘belong to’.
What is a universal set?
A set containing all elements relevant to a specific problem.
Denoted by U, it can contain various subsets under study.
What is a subset?
A set of which all the elements are contained in another set.
Example: If A = {1, 2, 3} and B = {1, 2}, then B is a subset of A.
What is a finite set?
A set with a finite number of elements that can be counted.
Example: Set A = {1, 2, 3} has 3 elements.
What is an infinite set?
A set with elements that cannot be counted, having an infinite number of elements.
Example: Set B = {1, 2, 3, …, ∞}.
What are equal sets?
Sets that contain the same elements regardless of order.
Example: Set A = {1, 2, 3} and Set B = {3, 1, 2}.
What is a null set?
A set that does not contain any elements, also called an empty set.
Example: Set N = {}.
What are proper and improper subsets?
Proper subsets contain some but not all elements of another set, while improper subsets can be equal to the set itself.
What is the formula for the number of subsets in a set
Formula = 2^n
n is the power.
What does the intersection of sets represent?
Intersection of sets → (AND)
The elements in the intersection are in both A and B.
What is the union of sets?
Union of sets → (OR)
A ∪ B includes all elements in A or B.
What is a Venn diagram?
A pictorial representation of sets in a plane.
What is a property of the union of sets?
1) A ∪ A = A
2) A ∪ (A ∪ B) = A
3) If A ⊆ B then A ∪ B = B
4) A ∪ (B ∪ C) = (A ∪ B) ∪ C
What does ‘U’ represent in set theory?
A universal set
What does ‘difference’ in sets mean?
The difference contains all elements in set A but not in set B.
Example: A = {1, 2, 3, 4, 5}, B = {3, 4, 5} → A - B = {1, 2}
What is the intersection of sets?
Both sets A and B have common elements.
What is a proper subset?
A proper subset is whereby A is a subset of B but A is not equal to B.
Example: If A = {1, 2} and B = {1, 2, 3}, then A is a proper subset of B.
What is an improper subset?
An improper subset is whereby the subset contains all elements from the original set.
Example: If A = {1, 2} and B = {1, 2}, then A is an improper subset of B.
