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Questions and Answers
What is a set?
What is a set?
A set is a collection of well-defined, distinct objects.
Objects in a set are called elements.
Objects in a set are called elements.
True (A)
Which of the following are examples of well-defined sets?
Which of the following are examples of well-defined sets?
Which of the following is NOT a well-defined set?
Which of the following is NOT a well-defined set?
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Which of the following is NOT a method for describing a set?
Which of the following is NOT a method for describing a set?
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What is the symbol for an empty or null set?
What is the symbol for an empty or null set?
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What type of set has a limited number of elements?
What type of set has a limited number of elements?
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What is cardinality of a set?
What is cardinality of a set?
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What is the symbol used to represent 'is a subset of'?
What is the symbol used to represent 'is a subset of'?
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Every set is a subset of itself.
Every set is a subset of itself.
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The empty set is a subset of every set.
The empty set is a subset of every set.
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What is the union of two sets?
What is the union of two sets?
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What is the intersection of two sets?
What is the intersection of two sets?
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Study Notes
What is a Set?
- A set is a collection of well-defined, distinct objects.
- Objects in a set are called elements.
Well-defined sets
- It is possible to determine if an object belongs to a well-defined set.
- Examples:
- A set of fruits.
- A set of counting numbers.
- A set of even numbers.
Not Well-defined Sets
- It is not possible to determine if an object belongs to a set that is not well-defined.
- Examples:
- The set of famous dancers.
- The set of honest people.
- The set of good writers.
Describing Sets
- Verbal Description Method: The set is described in words using a verbal statement.
- Roaster or Listing Method: The elements of the set are listed in a row separated by commas and enclosed with braces.
- Set Builder Notation: A mathematical notation for describing a set where you state the properties that its members must satisfy.
Types of Sets
- Finite Sets: A set with a limited number of elements that can be counted.
- Infinite Sets: A set with an unlimited number of elements that may or may not be counted.
- Empty or Null Sets: A set with no elements. The symbol is {} or { }.
- Universal Set: A set containing all relevant elements for a particular context. It is denoted by the symbol 'U'.
Cardinality of a Set
- The Cardinal number of a set 'A', denoted by N(A), is the number of elements in the set.
- It refers to the number of elements present in the set.
Sets and their elements
- A set is a collection of distinct objects called elements.
- Sets can be described in multiple ways:
- Verbal description method: Describes the elements using words.
- Listing method: Lists all the elements within curly braces.
- Set builder notation: Uses a statement to describe the elements.
Cardinality of a set
- The cardinality of a set is the number of its elements.
Subsets
- A set A is a subset of another set B if every element in A is also an element in B.
- This is represented using the symbol: ⊆ (read as "is a subset of").
- Every set is a subset of itself.
- The empty set (∅) is a subset of every set.
Union of sets
- The union of sets A and B (written as A ∪ B) includes all elements from both A and B.
- It is represented using the symbol: ∪ (read as "union").
Intersection of sets
- The intersection of sets A and B (written as A ∩ B) includes only the elements that are present in both A and B.
- It is represented using the symbol: ∩ (read as "intersection").
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Description
This quiz covers the concept of sets, including well-defined and not well-defined sets. It explores methods of describing sets, such as verbal descriptions and set builder notation. Test your understanding of finite and infinite sets with this informative quiz.
