Set Theory Lecture Review Flashcards

Vocabulary-style practice flashcards reviewing core set theory concepts, roster forms, interval representations, and subset calculations from the lecture.

Cardinality of Disjoint Set Difference $n(A - B)$

For two disjoint sets $A$ and $B$, the value of $n(A - B)$ is equal to $n(A)$. For example, if $n(A) = 4$ and $n(B) = 2$, then $n(A - B) = 4$.

Roster Form of Prime Numbers in Universal Set $U = \{1, 2, 3, 4, 5, 6, 7, 8\}$

The roster form of set $A = \{x : x \in U \text{ and } x \text{ is a prime number}\}$ is $\{2, 3, 5, 7\}$.

Proper Subsets Element Formula

The number of proper subsets of a set with $n$ elements is given by $2^n - 1$. If a set has $63$ proper subsets, solving $2^n - 1 = 63$ gives $n = 6$ elements.

Roster Form of Integers Between $-3$ and $7$

The roster form of set $A = \{x : x \text{ is an integer and } -3 < x < 7\}$ is $\{-2, -1, 0, 1, 2, 3, 4, 5, 6\}$.

Empty Set Cardinality Example

For set $A = \{x : x \text{ is a natural number}, x < 5 \text{ and } x > 7\}$, no natural number satisfies both conditions simultaneously, so $n(A) = 0$.

Set-Builder Form of Open Interval $(6, 12)$

The set-builder representation of the open interval $(6, 12)$ is $\{x : x \in \mathbb{R}, 6 < x < 12\}$.

Union of a Subset and Its Container Set

If $A$ and $B$ are two sets such that $A \subset B$, then their union $A \cup B$ is equal to $B$.

Subsets Count for Prime Numbers Less Than $10$

The set $A = \{x : x \text{ is a prime number less than } 10\}$ consists of $4$ elements: $\{2, 3, 5, 7\}$. The total number of subsets is $2^4 = 16$.

Number of Subsets of Set $A = \{1, 2, 3\}$

For a set $A$ with $3$ elements, the total number of subsets is given by $2^3 = 8$.

Number of Subsets of a Two-Element Set

If a set $A$ contains $2$ elements, the total number of subsets is calculated as $2^2 = 4$.