Sets

The set-builder form of $\{5, 10, 15, 20, 25\}$ is:

Which of the following collections is well-defined?

The roster form of the set $J = \{x : x = 2n-1, n \in \mathbb{N} \text{ and } n \leq 3\}$ is:

If $V$ is the set of vowels in English alphabet, then which is correct?

The roster form of the set $Y = \{x : x \in \mathbb{N} \text{ and } x \text{ is a factor of 15}\}$ is:

The set-builder form of the set $X = \{0, 1, 2, 3, 4, 5\}$ is:

The roster form of the set $W = \{x : x = 2n - 1, n \in \mathbb{N} \text{ and } n < 5\}$ is:

Which of the following represents the set $Q_1 = \{\frac{1}{2}, \frac{3}{10}, \frac{5}{26}, \frac{7}{50}\}$ in set-builder form?

The roster form of the set $P_1 = \{x \in \mathbb{Z} : x^2 \leq 9 \text{ and } x > 0\}$ is:

Which of the following describes $O_1 = \{2, 6, 10, 14, 18\}$ in set-builder form?

If $A = \{x : x^2 = 25\}$ and $B = \{5\}$, which of the following is correct?

The set of vowels in the English alphabet is:

Let $A = \{x : x \in \mathbb{N}, x+5 = 5\}$. This set is known as a/an:

The set of all squares of integers is:

Let $A = \{x \in \mathbb{Z} : x^3 - 6x^2 + 11x - 6 = 0\}$ and $B = \{1, 2, 3\}$. What is the relationship between set $A$ and set $B$?

The set $\{x : x \in \mathbb{N}, x \text{ is a multiple of 7 and } x < 5\}$ is:

Let $A = \{x : x \in \mathbb{Z}, x^2 < 1\}$ and $B = \{0\}$. Which statement is correct?

Let $A = \{n \in \mathbb{N} : n \text{ is a factor of } 6\}$ and $B = \{x \in \mathbb{Z} : (x-1)(x-2)(x-3)(x-6) = 0\}$. Which is true?

Let $A = \{x \in \mathbb{Z} : |x-2| < 1\}$. The set $A$ is:

Consider $A = \{x \in \mathbb{R} : \sin x = 2\}$ and $B = \{x \in \mathbb{Q} : x^2 = 3\}$. Which statement is true?

If a set has 0 elements, the total number of proper subsets is:

The set of natural numbers $\mathbb{N}$ is a subset of which of the following?

If $S = \{a, b, c\}$, which of the following is an element of the power set $P(S)$?

If $A \subset B$ and $B \subset C$, then $A$ is a _____ of $C$.

Let $A$ be the set of all squares in a plane and $B$ be the set of all rectangles in the same plane. Then:

If $A$ is a set with $n(A) = 4$, how many subsets of $A$ have at least 3 elements?

Given $A = \{a, b, \{c, d\}, e\}$, which statement is true?

If $X = \{ \emptyset, \{\emptyset\} \}$, which of the following is FALSE?

How many subsets of $A = \{1, 2, 3, 4, 5\}$ have a sum of elements equal to 10?

Let $A$ be a set with $n(A) = 3$. Find the number of elements in $P(P(A)) \cap P(A)$. (Assume elements of $A$ are not sets).

The operation $(A \cup B) \cap A$ always results in which set?

If $n(A) = 15$ and $n(B) = 20$, what is the minimum possible value for $n(A \cup B)$?

If $n(A) = 15$ and $n(B) = 20$, what is the maximum possible value for $n(A \cap B)$?

In a Venn diagram, the region $A \cap (B \cup C)$ represents the elements that are in $A$ AND in:

The region $(A \cap B) \cup (A - B)$ is equal to which set?

If $n(A-B) = 18, n(B-A) = 25$ and $n(A \cap B) = 15$, find $n(A \cup B)$.

Let $n(U) = 50, n(A) = 20, n(B) = 25$. If $n(A \cup B) = 40$, find $n(A' \cap B')$.

What is the relationship between $(A \cup B)'$ and $A' \cap B'$ according to De Morgan's Law?

In a group of 100 people, 70 like apples and 60 like mangoes. What is the maximum possible number of people who like both?

If $n(A) = 15, n(B) = 25$, what is the minimum possible value of $n(A \Delta B)$?

Let $A = \{1, 2\}$ and $B = \{3, 4\}$. Then $A \cup B$ is:

If $A = \{x : x \in \mathbb{N}, x \text{ is a multiple of 5}\}$ and $B = \{5, 10, 15\}$, find $B - A$.

Which of the following describes $A \cap A$?

If $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7, 8\}$, what is $A - (A \cap B)$?

Given $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$. Which of the following is equal to $(A - B) \cap (B - A)$?

If $n(A) = 12, n(B) = 8$ and $n(A \cap B) = 4$, then $n((A - B) \cup (B - A))$ is:

For any two sets $A$ and $B$, $A \cap (A \cup B)'$ is:

Simplify $(A \cap B) \cup (A - B)$.

If $A \cap B = B$, then which of the following is true?

If $n(A) = 10$, $n(B) = 15$ and $n(C) = 20$. If $A, B, C$ are pairwise disjoint, find $n(A \cup B \cup C)$.

If two sets $A$ and $B$ are such that $A \cap B = \emptyset$ and $A \cup B = U$, then $B$ must be the:

In a Venn diagram, the region representing $A'$ is:

If $A = \{x : x \text{ is a factor of } 6\}$ and $U = \{1, 2, 3, 4, 5, 6\}$, then $A'$ is:

Given $U = \{10, 11, 12, 13\}$ and $A' = \{10, 11\}$, find set $A$.

If $U = \{1, 2, 3, 4, 5, 6\}$ and $A = \{1, 3, 5\}$, what is the number of elements in the power set of $A'$, i.e., $n(P(A'))$?

Let $U$ be the set of all integers and $A$ be the set of all positive integers. Then $A'$ is the set of:

If $A \subset U$ and $B \subset U$, then $(A \cap B')'$ is equivalent to:

Identify the shaded region in a Venn diagram representing $(A' \cup B') \cap (A \cap B)$.

If $U = \{1, 2, 3, 4, 5\}$ and $A = \{1, 2\}$, how many elements are in $P(U) - P(A')$?

The set of real numbers $\mathbb{R}$ is the universal set. If $A = \{x : x^2 + 1 = 0\}$, find $A'$.

In a group of $130$ people, $80$ play football and $70$ play cricket. If every person plays at least one game, how many play both?

If $n(X) = 14$, $n(X \cup Y) = 25$, and $n(X \cap Y) = 6$, find $n(Y)$.

If $n(A) = 55$ and $n(B) = 35$, and the sets are disjoint, what is $n(A \cup B)$?

In a group of $60$ people, $35$ like oranges and $30$ like grapes. If every person likes at least one, how many like both?

In a gym with $130$ members, $70$ do cardio exercises and $60$ do weight training. If $20$ members do neither, how many members do both cardio and weight training?

At a party of $20$ people, $15$ drink tea and $12$ drink coffee. If $5$ people drink neither, how many drink both tea and coffee?

A survey of $50$ people found that $28$ read Magazine A and $26$ read Magazine B. If $8$ read both magazines, how many read at least one magazine?

In a survey of $100$ people, $40$ like product A and $50$ like product B. Let $x$ be the maximum value of $n(A \Delta B)$ and $y$ be the minimum value of $n(A \Delta B)$. Find $x - y$.

If $n(A \cap B) = 1/3 n(A)$ and $n(A \cap B) = 1/4 n(B)$, and $n(A \cup B) = 120$, find $n(A \cap B)$.

In a survey of $500$ people, $285$ read magazine A and $195$ read magazine B. If $115$ read neither, find the number of people who read both.

The number $22/7$ is an element of which set?

Which symbol represents the set of all whole numbers?

The intersection of $(0, 5)$ and $(2, 7)$ is:

Which interval represents all real numbers $x$ such that $x$ is at most $7$?

If $A = ( -3, 0 ]$ and $B = [ 0, 3 )$, what is $A \cup B$?

Identify the set represented by $( -\infty, 5 ] \cap [ 5, \infty )$.

Express the set $\{x \in \mathbb{R} : x^2 \geq 0\}$ in interval notation.

Express the set $\{x \in \mathbb{R} : x^2 - 5x + 4 > 0\}$ using interval notation.

Let $A = \{x \in \mathbb{R} : x = 1/n, n \in \mathbb{N}\}$. What is $A \cap (0, 0.1]$?

Find the complement of the set $A = \{x \in \mathbb{R} : 1 < x^2 < 4\}$ in the set $(0, \infty)$.

The intersection of the set of real numbers $\mathbb{R}$ and the interval $[2, 5]$ is:

Is the number $\sqrt{2}$ contained in the interval $[1, 2]$?

Find the length of the interval $[-\pi, \pi]$.

Write the set builder form for the interval $(-\infty, 3]$.

If $x \in (1, 4)$, then what can be said about $x^2$?

The difference between an open interval $(a, b)$ and a closed interval $[a, b]$ is:

Identify the interval notation for $\{x : x \in \mathbb{R}, x \leq 4 \text{ and } x \geq 4\}$.

If $x \in [2, 4]$ and $y \in [1, 3]$, find the interval representing all possible values of $x - y$.

Let $A = (1, 5)$ and $B = [2, 6]$. Find the set of all integers in $A \cap B$.

Solve the inequality $|x| < 0$.