Sets and Functions

Which German mathematician first explained the concept of set?

In which years did George Cantor live?

Cantor created a sensation in mathematical science by introducing—

A set is best described as—

Sets are usually denoted by—

Each object or member of a set is called its—

If $a$ is an element of set $B$, it is written as—

If $c$ is not an element of set $B$, it is written as—

The two methods of expressing a set are—

In the roster method, elements are—

In the set-builder method, elements are—

Set-builder method is also called—

In set-builder notation, the symbol : is read as—

$A = \{7, 14, 21, 28\}$ in set-builder form is—

$B = \{x : x$ is a divisor of $28\}$ in roster form is—

$C = \{x : x$ is a positive integer and $x^2 < 18\}$ in roster form is—

Which of the following is a correct roster-form set?

$\{-9, -6, -3, 3, 6, 9\}$ in set-builder form can be written as—

A set whose number of elements can be determined by counting is called—

A set whose elements cannot be listed by counting is called—

How many elements does $D = \{x, y, z\}$ have?

$E = \{3, 6, 9, \dots, 60\}$ has how many elements?

Which of the following is an infinite set?

Which of the following is a finite set?

$\{3, 3^2, 3^3, \dots\}$ is a—

$\{x : x$ is an integer and $x < 4\}$ is—

$\{y : y \in \mathbb{N}$ and $y^2 < 100 < y\}$ is—

In the proof that $\mathbb{N}$ is infinite, the contradiction arises because—

An empty set is a set with—

The empty set is denoted by—

Which of the following is an empty set?

$\{x \in \mathbb{N} : x$ is prime and $23 < x < 29\}$ equals—

Which set is NOT empty?

Who first expressed sets using pictures?

In which years did John Venn live?

In a Venn diagram, sets are usually represented by—

If $B$ is a subset of $A$, it is written—

The empty set is a subset of—

Every set is a subset of—

How many subsets does $A = \{a, b\}$ have?

How many subsets does a set of $n$ elements have?

How many proper subsets does a set of $n$ elements have?

How many subsets does $P = \{x, y, z\}$ have?

How many proper subsets does $P = \{x, y, z\}$ have?

Of the subsets of a set, proper subsets are those that—

The empty set $\varnothing$ is—

Which of the following is NOT a proper subset of $P = \{x, y, z\}$?

Two sets $A$ and $B$ are equal if and only if—

If elements of $A$ are reordered or repeated, the set—

$A = \{3, 5, 7\}$, $B = \{5, 3, 3, 7\}$, $C = \{7, 7, 3, 5, 5\}$. Which is true?

$A - B$ is defined as—

$A \setminus B$ is another notation for—

If $A = \{1, 2, 3, 4, 5\}$ and $B = \{3, 5\}$, then $A - B =$

If $P = \{1, 2, 3, 4, 6, 12\}$ and $Q = \{3, 6, 9, 12\}$, then $P - Q =$

For any set $A$, $A - A$ equals—

For any set $A$, $A - \varnothing$ equals—

If every set under discussion is a subset of a fixed set, that fixed set is called the—

The universal set is usually denoted by—

If $C = \{2, 4, 6, \dots\}$ (even naturals), a suitable universal set is—

If $U$ is universal and $A \subset U$, the complement of $A$ is—

The complement of $A$ is denoted by—

If $U = \{1, 2, 3, 4, 5, 6, 7\}$ and $A = \{2, 4, 6, 7\}$, then $A^c =$

If $U = \{1, 2, 3, 4, 5, 6, 7\}$ and $B = \{1, 3, 5\}$, then $B^c =$

For any set $A$ and universal $U$, $(A^c)^c$ equals—

$U^c$ equals—

The union of two sets $A$ and $B$ is—

$A \cup B$ is read as—

If $C = \{3, 4, 5\}$ and $D = \{4, 6, 8\}$, then $C \cup D =$

For any set $A$, $A \cup \varnothing$ equals—

For any set $A$, $A \cup A$ equals—

If $A$ is the set of factors of $35$ and $B$ is the set of factors of $45$, then $A \cup B =$

The intersection of $A$ and $B$ is defined as—

$A \cap B$ is read as—

If $P = \{x \in \mathbb{N} : 2 < x \le 6\}$ and $Q = \{x \in \mathbb{N} : x$ is even and $x \le 8\}$, then $P \cap Q =$

For any set $A$, $A \cap \varnothing$ equals—

For any set $A$, $A \cap A$ equals—

If $A$ is the set of factors of $35$ and $B$ is the set of factors of $45$, then $A \cap B =$

Two sets are called disjoint if—

If $A = \{1, 2, 3\}$ and $B = \{4, 5\}$, then $A \cap B =$

Which pair of sets is disjoint?

De Morgan's law states $(A \cup B)^c$ equals—

De Morgan's law states $(A \cap B)^c$ equals—

The distributive law $(A \cup B) \cap C$ equals—

The distributive law $(A \cap B) \cup C$ equals—

$A \cup B = (A \setminus B) \cup (B \setminus A) \cup (A \cap B)$ is a—

The power set of $A$ is—

The power set of $A$ is denoted by—

If $A = \varnothing$, then $P(A)$ has how many elements?

If $A = \{a\}$, then $P(A)$ has how many elements?

If $A = \{a, b\}$, then $P(A)$ has how many elements?

If a set has $n$ elements, its power set has—

If $G = \{1, 2, 3\}$, the number of elements in $P(G)$ is—

If $B = \{0, 1, 2, 3\}$, the number of elements in $P(B)$ is—

If $A = \{1, 2\}$ and $B = \{2, 5\}$, the number of elements of $P(A \cap B)$ is—

For an ordered pair, the pair $(x, y)$ equals $(a, b)$ if and only if—

$(2, 3)$ and $(3, 2)$ are—

If $(2x + y, 3) = (6, x - y)$, then $x$ and $y$ are—

If $(x - 1, y + 2) = (y - 2, 2x + 1)$, then $(x, y)$ is—

If $(6x - y, 13) = (1, 3x + 2y)$, then $(x, y)$ is—

The Cartesian product $A \times B$ is defined as—

$A \times B$ is read as—