Podcast
Questions and Answers
Given set A = {2, 4, 6, 8, 10} and set B = {1, 2, 3, 4, 5}, what is the intersection of A and B?
Given set A = {2, 4, 6, 8, 10} and set B = {1, 2, 3, 4, 5}, what is the intersection of A and B?
- {1, 2, 3, 4, 5, 6, 8, 10}
- {6, 8, 10}
- {1, 3, 5}
- {2, 4} (correct)
Which of the following notations correctly represents the union of set X and set Y?
Which of the following notations correctly represents the union of set X and set Y?
- X ∩ Y
- X \ Y
- X ∪ Y (correct)
- X'
- None of the above
If set P represents all even numbers and set Q represents all prime numbers, how would you describe the intersection of P and Q?
If set P represents all even numbers and set Q represents all prime numbers, how would you describe the intersection of P and Q?
- The set containing all odd prime numbers
- The empty set
- The set containing all even prime numbers (correct)
- The set containing all composite numbers
Consider set R = {a, b, c, d} and set S = {c, d, e, f}. What elements are present in the union of R and S?
Consider set R = {a, b, c, d} and set S = {c, d, e, f}. What elements are present in the union of R and S?
Given A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, which set represents A ∪ B (the union of sets A and B)?
Given A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, which set represents A ∪ B (the union of sets A and B)?
Flashcards
What is a set?
What is a set?
A collection of distinct objects, considered as an object in its own right.
What is set notation?
What is set notation?
A concise and precise way to express mathematical ideas using symbols and conventions to define sets and their elements.
What is a union of sets?
What is a union of sets?
A union combines elements from two sets into one. A ∪ B includes all elements in A or B (or both).
What is an intersection of sets?
What is an intersection of sets?
Signup and view all the flashcards
What is a set complement?
What is a set complement?
Signup and view all the flashcards
Study Notes
- A set is a collection of objects, with the objects being called elements of the set.
- Set notation forms the basis of mathematical communication, being concise and precise.
- "α ε B" means "a is an element of B".
- "BC" means "B is a subset of C".
- "C2B" means "C contains B as a subset".
- Putting a slash through a symbol negates it; for example, "q∉B" means "q is not an element of B".
- A set of A = {1,2,3} and a set of B ={1,2,a,b }, and a set of c ={ a, b} are examples of sets.
Unions of Sets:
- A U B means {things that are in A or B}, which can be written as { x | x ∈ A or x ∈ B }.
- This is the set of x such that x is an element of A, or x is an element of B.
Intersection of Sets:
- A ∩ B includes things that are in both A and B, and it can be represented as { x | x ∈ A and x ∈ B }.
- This is the set of X such that is an element of A and X is also an element of B.
- For example, given A = {1,2,3}, B = {1,2,a,b}, and C = {a,b}, A U B = {1,2,3,a,b}, A ∩ B = {1,2}, and B ∩ C = {a, b}.
- Ø represents the empty set.
Set Complement:
- A \ B includes things that are in A but not in B, represented as { x | x ∈ A and x ∉ B }.
- This is the set of x such that x is an element of A, and x is not an element of B.
- For example, given A = {1,2,3} and B = {1,2,a,b}, A\B = {3} and B\A = {a,b}.
Sets of Numbers:
- The set of natural numbers is symbolized by N = {0, 1, 2, 3,...}.
- The set of integers is Z = {..., -2, -1, 0, 1, 2, 3,...}.
- The set of rational numbers is Q = { a/b | a ∈ Z and b ∈ Z, b ≠0 }.
- The set of real numbers is denoted by R.
- Real numbers (R) are ordered: if a, b ∈ R, then either a < b, a > b, or a = b.
- Each real number has a modulus, called absolute value.
- This is the distance from a to 0 on the number line.
Intervals (Subsets of R):
- [a, b] = {x ∈ R | a ≤ x and x ≤ b}
- (a, b) = {x ∈ R | a < x and x < b}
- [a, b) = {x ∈ R | a ≤ x and x < b}
- [a, ∞) = {x ∈ R | x ≥ a}
- (a, ∞) = {x ∈ R | x > a}
- (-∞, b] = {x ∈ R | x ≤ b}
- ∞ and -∞ are not elements of R, they are convenient notations.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
