Understanding Sets: Elements, Definitions, and Types

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Questions and Answers

Match the set operation with its correct definition:

Union = Elements in A, or in B, or in both. Intersection = Elements in both A and B. Difference = Elements in A but not in B. Symmetric Difference = Elements in either A or B, but not in their intersection.

Match the type of set with its characteristic:

Empty Set = Contains no elements. Singleton Set = Contains exactly one element. Finite Set = Contains a countable number of elements. Infinite Set = Contains an unlimited number of elements.

Match the set notation with its corresponding description:

$A = {x \mid x \in \mathbb{Z}, x > 0}$ = Set of all positive integers. $B = {2, 4, 6, 8}$ = Set of the first four positive even numbers. $C = {x \mid x^2 = 4}$ = Set of solutions to the equation $x^2 = 4$. $D = {}$ = The empty set.

Match the example with the correct set characteristic:

Set of all even numbers = Infinite Set Solution set of the equation $x + 5 = 0$ = Singleton Set Set of students in a classroom = Finite Set Set of all numbers that satisfy $x \neq x$ = Empty Set Signup and view all the answers

Match the symbolic representation with the verbal description of sets:

$A \cup B$ = The set containing all elements in A, B, or both. $A \cap B$ = The set containing only elements present in both A and B. $A \setminus B$ = The set containing elements in A but not in B. $B \setminus A$ = The set containing elements in B but not in A. Signup and view all the answers

Match the following set operations with their equivalent expressions, given the symmetric difference $A \Delta B = (A - B) \cup (B - A)$:

$(A \Delta B) \Delta C$ = $(A \cup B \cup C) - (A \cap B) - (A \cap C) - (B \cap C)$ $A \Delta A$ = $\emptyset$ $A \Delta \emptyset$ = $A$ $A \Delta U$ = $A'$ Signup and view all the answers

Match the following set identities with their corresponding descriptions:

$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ = Distributive Law of union over intersection $(A \cap B)' = A' \cup B'$ = De Morgan's Law for intersection $A \cup A' = U$ = Complement Law $A \cap U = A$ = Identity Law involving the universal set Signup and view all the answers

Match each set operation on set A with the resulting cardinality, given $|A| = n$:

$|P(A)|$ = $2^n$ $|A \cup A'|$ = $|U|$ $|A \cap A'|$ = $0$ $|A \cup \emptyset|$ = $n$ Signup and view all the answers

Match the following descriptions of set relationships with their correct symbolic representation:

A is a subset of B = $A \subseteq B$ A is a proper subset of B = $A \subset B$ The intersection of A and B is empty = $A \cap B = \emptyset$ The union of A and B is the universal set = $A \cup B = U$ Signup and view all the answers

Match the following applications with the corresponding area of use:

Data organization and querying = Databases Representing logical conditions = Propositional Logic Evaluating likelihood of events = Probability Theory Designing efficient algorithms = Computer Science Signup and view all the answers

Flashcards

Symmetric Difference

Elements in A or B but not both. (A - B) ∪ (B - A)

Commutative Law

Changing the order of sets doesn't affect the result.