(a)

\begin{align*} B & = \{ 1, 3, 5, 7, 9 \} \end{align*}

(b)(i)

$$ \text{True} $$

(b)(ii)

$$ \text{True} $$

(b)(iii)

$$ \text{False} $$

(b)(iv)

$$ \text{True} $$

(a) Note that the numbers 1 and 10 are excluded

\begin{align*} A & = \{ 2, 3, 4, 5, 6, 7, 8, 9 \} \end{align*}

(b)

\begin{align*} B & = \{ -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 \} \end{align*}

(c)

\begin{align*} C & = \{ 2, 4, 6, 8, 10, 12 \} \end{align*}

(d) Vowels are the letters A E I O U

\begin{align*} D & = \{ \text{A} \} \end{align*}

(a)

\begin{align*} E & = \{ \} \\ \\ \text{Yes, } & E \text{ is an empty set} \end{align*}

(b)

\begin{align*} F & = \{ \} \\ \\ \text{Yes, } & F \text{ is an empty set} \end{align*}

(c) Quadrilaterals have 4 sides and thus 4 vertices. A pentagon has 5 sides and thus 5 vertices.

\begin{align*} G & = \{ \} \\ \\ \text{Yes, } & G \text{ is an empty set} \end{align*}

(d)

\begin{align*} H & = \{ 2 \} \\ \\ \text{No, } & H \text{ is not an empty set} \end{align*}

(a)

\begin{align*} D & = \{ \text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} \} \end{align*}

(b)(i)

\begin{align*} \text{Tuesday} \in D \end{align*}

(b)(ii)

\begin{align*} \text{Sunday} \in D \end{align*}

(b)(iii)

\begin{align*} \text{March} \notin D \end{align*}

(b)(iv)

\begin{align*} \text{Holiday} \notin D \end{align*}

(i)

$$ \text{No (since } \sqrt{50} = 7.0711) $$

(ii)

\begin{align*} P & = \{ 2^2, 3^2, 4^2, 5^2, 6^2, 7^2 \} \\ & = \{ 4, 9, 16, 25, 36, 49 \} \end{align*}

(a)

\begin{align*} I & = \{ \text{Red, Orange, Yellow, Green, Blue, Indigo, Violet} \} \end{align*}

(b)

\begin{align*} J & = \{ \text{New Year's Day, Chinese New Year, Good Friday, Labour Day, Vesak Day, Hari Raya Puasa, } \\ & \phantom{=0} \text{National Day, Hari Raya Haji, Deepavali, Christmas Day} \} \end{align*}

(c)

\begin{align*} K & = \{ \text{S, Y, M, T, R} \} \end{align*}

(d)

\begin{align*} L & = \{ \text{Mr/Miss/Mrs/Madam ______________} \} \end{align*}

(a)

$$ M \text{ is the set of non-negative even numbers} $$

(b)

$$ N \text{ is the set of non-negative even numbers up to and including 8} $$

(c)

$$ O = \{ 1^3, 2^3, 3^3, 4^3, 5^3, ... \} $$ $$ O \text{ is the set of perfect cubes} $$

(d)

$$ P \text{ is the set of multiples of } 5 $$

(a) Perfect squares are 1, 4, 9, 25, 36, ... while perfect cubes are 1, 8, 27, 64, 125, ...

\begin{align*} Q & = \{ \} \\ \\ R & = \{ 1 \} \end{align*}

(b)

\begin{align*} Q & = \emptyset \\ \\ R & \ne \emptyset \end{align*}

(i)

$$ \text{False. } c \text{ is in the set } \{ c, a, r \} $$

(ii)

$$ \text{False. The word } car \text{ is not in the set } \{ c, a, r \} $$

(iii)

$$ \text{False. } \{ c \} \text{ represents a set with a single element } c $$

(iv)

$$ \text{False. } \{ c, a, r \} \text{ is a set and not equals to a number} $$

(a)

$$ S = \{ x : x \text{ is a girl in my current class who wear spectacles} \} $$

(b)

$$ T = \{ x : x \text{ is a prime number} \} $$

(c)

$$ U = \{ x : x \text{ is a multiple of } 4 \} $$

(d)

$$ V = \{ x : x \text{ is a multiple of } 4 \text{ and } -8 \le x \le 12 \} $$

(i)

$$ \text{False. The set } \{ 0 \} \text{ contains a single element, } 0 $$

(ii)

$$ \text{True} $$

(iii)

$$ \text{False. The set } \{ \emptyset \} \text{ contains a single element, the symbol } \emptyset \text{. Thus, it is not an empty set} $$

(iv)

$$ \text{True} $$