Multiple Choice

1. Which of the following collections represents a well-defined set in mathematics?

   The collection of all odd numbers between $10$ and $20$.

   The collection of all interesting movies released this year.

   The collection of all students who love math.

   The collection of all the happiest children in the city.

2. Set $A$ is defined as the set of positive whole numbers that are factors of $12$. Express Set $A$ using the Roster Method.

   $A = \{1, 2, 3, 4, 6, 8, 12\}$

   $A = \{1, 2, 3, 4, 6\}$

   $A = \{1, 2, 3, 4, 6, 12\}$

   $A = \{2, 3, 4, 6, 12\}$

3. Given the set $B = \{x \mid x \text{ is a prime number and } 5 < x < 15\}$. Which of the following correctly lists the elements of set $B$?

   $B = \{7, 9, 11, 13\}$

   $B = \{6, 8, 10, 12, 14\}$

   $B = \{5, 7, 11, 13, 15\}$

   $B = \{7, 11, 13\}$

4. Which set-builder notation correctly describes the set $S = \{4, 8, 12, 16\}$?

   $S = \{x \mid x \text{ is an even number less than } 18\}$

   $S = \{x \mid x \text{ is a number } n, \text{ such that } n = 4k, \text{ for } k = 1, 2, 3, 4, 5\}$

   $S = \{x \mid x \text{ is a multiple of } 4 \text{ and } x \leq 16\}$

   $S = \{x \mid x \text{ is a multiple of } 2 \text{ and } x < 17\}$

5. Let $M = \{5, 10, 15, 20\}$. Which statement about set $M$ is TRUE?

   $12 \in M$

   $20 \notin M$

   $13 \notin M$

   $\{5\} \in M$

6. Which of the following options correctly represents the Empty Set (Null Set)?

   $\{0\}$

   $E$

   $\{\emptyset\}$

   $\emptyset$

7. Which of the following describes a Finite Set?

   The set of all fractions between $0$ and $1$.

   The set of all whole numbers greater than $100$.

   The set of capital cities of all countries in the world.

   The set of all integers.

8. Which of the following sets is an Infinite Set?

   The set of solutions for the equation $x^2 = 9$.

   The set of days in the month of July.

   The set of points on a straight line segment.

   The set of letters in the English alphabet.

9. Which of the following sets is a Singleton Set?

   $X = \{x \mid x \text{ is an even prime number}\}$

   $X = \{x \mid x \text{ is an odd prime number}\}$

   $X = \{x \mid x \text{ is an integer between } 3 \text{ and } 5\}$

   $X = \{x \mid x \text{ is a whole number and } x^2 = 4\}$

10. If Set $A = \{1, 3, 5\}$ and Set $B = \{2, 4, 6\}$, which set could serve as the Universal Set ($U$) for $A$ and $B$ in this specific context?

    $U = \text{The set of all prime numbers}$

    $U = \{1, 2, 3, 4\}$

    $U = \text{The set of all natural numbers up to } 10$

    $U = \{0, 1, 2, 3, 4, 5\}$

11. Given the set $P = \{P, R, O, B, L, E, M\}$. What is the cardinality of set $P$, denoted $n(P)$?

    $n(P) = 5$

    $n(P) = 7$

    $n(P) = 8$

    $n(P) = 6$

12. Calculate the cardinality of set $K$, where $K = \{x \mid x \text{ is an integer and } -3 \leq x < 2\}$.

    $n(K) = 3$

    $n(K) = 6$

    $n(K) = 4$

    $n(K) = 5$

13. Set $A = \{m, a, t, h\}$. Which of the following options is NOT a subset of $A$?

    $\{m, a, t, h\}$

    $\{a, h\}$

    $\emptyset$

    $\{m, a, t, i, c\}$

14. Let $R = \{1, 2, 3\}$. Which of the following is a proper subset of $R$?

    $\{1, 2, 3\}$

    $R$

    $\{2, 3\}$

    $\{4\}$

15. A set $T$ has $4$ elements. How many total subsets can be formed from set $T$?

    $4$

    $8$

    $12$

    $16$

16. Which pair of sets below are considered Equal Sets?

    $A = \{1, 2, 3\}$ and $B = \{1, 2, 3, 4\}$

    $G = \{5, 10, 15\}$ and $H = \{15, 5, 10\}$

    $E = \{r, a, c, e\}$ and $F = \{c, a, r\}$

    $C = \{p, i, e\}$ and $D = \{p, i, z, z, a\}$

17. Which pair of sets below are considered Equivalent Sets?

    $A = \{1, 2, 3, 4\}$ and $B = \{4, 3, 2\}$

    $G = \{T, O, P\}$ and $H = \{1, 2, 3\}$

    $C = \{a, b, c\}$ and $D = \{c, b, d, e\}$

    $E = \{1, 2\}$ and $F = \{1, 2, 3\}$

18. Set $V$ is defined as the set of vowels in the English alphabet. Which expression correctly represents the total number of subsets of $V$?

    $2 \times n(V)$

    $5^2$

    $n(V)$

    $2^5$

19. Let $W = \{x \mid x$ is a whole number $\}$. Which of the following statements is FALSE?

    $0 \in W$

    $\{-1\} \subseteq W$

    $W$ is an infinite set.

    $1.5 \notin W$

20. When describing sets, which characteristic is NOT required for two sets to be considered Equal Sets?

    They must have the same number of elements (same cardinality).

    Every element of the first set must belong to the second set.

    The elements must be listed in the same order.

    Every element of the second set must belong to the first set.

21. Which of the following collections represents a well-defined set?

    The collection of all even numbers between $10$ and $20$.

    The collection of delicious fruits.

    The collection of all highly intelligent animals.

    The collection of all nice students in the class.

22. The set $P = \{x \mid x \text{ is a counting number less than } 5\}$ is written in Roster method as:

    $P = \{0, 1, 2, 3, 4, 5\}$

    $P = \{0, 1, 2, 3, 4\}$

    $P = \{1, 2, 3, 4, 5\}$

    $P = \{1, 2, 3, 4\}$

23. Given the set $A = \{5, 10, 15, 20\}$, which statement uses the correct standard set notation?

    $25 \notin A$

    $10 \notin A$

    $\{5\} \in A$

    $50 \in A$

24. Calculate the cardinality of the set $D = \{\text{Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}\}$.

    $n(D) = 9$

    $n(D) = 8$

    $n(D) = 1$

    $n(D) = 7$

25. Which of the following sets is a finite set?

    $S = \{x \mid x \text{ is an integer greater than } 100\}$

    $V = \{\text{all points on a straight line}\}$

    $R = \{\text{months of the year}\}$

    $T = \{\text{all prime numbers}\}$

26. Which set represents the Empty Set ($\emptyset$)?

    $B = \{x \mid x \text{ is a whole number and } x < 1\}$

    $A = \{0\}$

    $D = \{x \mid x \text{ is an odd number divisible by } 2\}$

    $C = \{x \mid x \text{ is an even prime number}\}$

27. A set containing exactly one element is called a Singleton Set. Which of the following is a Singleton Set?

    The set of positive divisors of $6$.

    The set of natural numbers less than $1$.

    The set of whole numbers $x$ such that $5 < x < 7$.

    The set of prime numbers less than $4$.

28. If the Universal Set $U$ is defined as the set of all integers, which of the following sets is NOT a reasonable subset within this context?

    The set of all integers divisible by $5$.

    The set of all negative integers.

    The set of all irrational numbers.

    The set of all whole numbers.

29. Let $K = \{y \mid y = 2n - 1, \text{ where } n \in \{1, 2, 3, 4, 5\}\}$. What is the cardinality of set $K$, $n(K)$?

    $n(K) = 9$

    $n(K) = 10$

    $n(K) = 6$

    $n(K) = 5$

30. Given $A = \{a, b, c\}$ and $B = \{a, b, c, d\}$, which statement correctly describes the relationship between the sets using subset notation?

    $d \in A$

    $\{a\} \in A$

    $A \subseteq B$

    $B \subseteq A$

31. Set $X = \{10, 20, 30\}$. Which set $Y$ is a proper subset ($Y \subset X$)?

    $Y = \{10, 20, 30\}$

    $Y = \{10, 20, 30, 40\}$

    $Y = \{10, 20\}$

32. Two sets are equal if they contain exactly the same elements. If $M = \{5, 1, 9, 3\}$ and $N = \{x, 9, 5, 1\}$, what value must $x$ have for $M$ and $N$ to be equal sets ($M=N$)?

    $x = 5$

    $x = 0$

    $x = 3$

    $x = 1$

33. Which pair of sets is Equivalent but NOT Equal?

    $A = \{r, s, t, u\}$ and $B = \{1, 2, 3, 4\}$

    $A = \{a, b\}$ and $B = \{b, a\}$

    $A = \{1, 2, 3\}$ and $B = \{1, 2, 3\}$

    $A = \{10\}$ and $B = \{10\}$

34. If $S = \{x^2 \mid x \text{ is an integer and } -2 \le x \le 2\}$, what is the cardinality $n(S)$?

    $n(S) = 5$

    $n(S) = 6$

    $n(S) = 3$

    $n(S) = 2$

35. Set $G$ has a cardinality of $n(G) = 4$. How many total subsets (including the set itself and the empty set) can be formed from set $G$?

    $8$

    $10$

    $4$

    $16$