(i)

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

(ii)(a)

\begin{align} \text{True} \end{align}

(ii)(b)

\begin{align} \text{True} \end{align}

(ii)(c)

\begin{align} \text{False} \end{align}

(ii)(d)

\begin{align} \text{True} \end{align}

(iii)

\begin{align} n(A) & = 5 \phantom{000000} [\text{5 elements in set } A] \end{align}

(a)

\begin{align} B & = \{ 2, 3, 4, 5, 6, 7, 8, 9 \} \\ \\ n(B) & = 8 \end{align}

(b)

\begin{align} C & = \{ -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 \} \\ \\ n(C) & = 10 \end{align}

(c)

\begin{align} D & = \{ 2, 4, 6, 8, 10, 12 \} \\ \\ n(D) & = 6 \end{align}

(d)

\begin{align} E & = \{ \text{A} \} \phantom{000000} [\text{Vowels: A, E, I, O, U} ] \\ \\ n(E) & = 1 \end{align}

(a)

\begin{align} F & = \{ \text{red, orange, yellow, green, blue, indigo, violet} \}\\ \\ n(F) & = 7 \end{align}

(b)

\begin{align} G & = \{ \text{New Year's Day, CNY (2 days), Good Friday, Labour Day, Hari Raya Puasa,} \\ & \phantom{0000} \text{Hari Raya Haji, National Day, Deepavali, Christmas Day} \} \\ \\ n(G) & = 10 \end{align}

(c)

\begin{align} H & = \{ \text{S, Y, M, T, R} \} \\ \\ n(H) & = 5 \end{align}

(a)

\begin{align} K & = \emptyset \phantom{000000} [\text{Odd numbers are not divisible by 2}] \end{align}

(b)

\begin{align} L & = \{ 2 \} \end{align}

(c)

\begin{align} M & = \emptyset \phantom{000000} [\text{Quadrilaterals have 4 sides, thus have 4 vertices}] \end{align}

(d)

\begin{align} N & = \emptyset \end{align}

(i)

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

(ii)(a)

\begin{align} \text{Tuesday} & \in P \end{align}

(ii)(b)

\begin{align} \text{Sunday} & \in P \end{align}

(ii)(c)

\begin{align} \text{March} & \notin P \end{align}

(ii)(d)

\begin{align} \text{Holiday} & \notin P \end{align}

(iii)

\begin{align} n(P) & = 7 \end{align}

(i)

\begin{align} \sqrt{10} & = 3.162 \\ \\ \therefore 10 & \notin Q \end{align}

(ii)

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

(iii)

\begin{align} n(Q) & = 6 \end{align}

(i)

\begin{align} & R \text{ is the set of non-negative even integers} \\ \\ & S \text{ is the set of non-negative even integers less than 10} \end{align}

(ii)

\begin{align} n(R) \text{ is undefined} & \text{ while } n(S) = 5 \\ \\ \therefore n(R) \ne n(S) \end{align}

(iii)

\begin{align} \text{No, since } R \text{ contains infinite number of non-negative integers while } S \text{ contains the first 5 non-negative integers} \end{align}

(i)

\begin{align} T & = \{ \} = \emptyset \phantom{000000} [ 3^2 = 9, 4^2 = 16] \\ \\ U & = \{ 1 \} \phantom{000000000} [1^2 = 1^3 = 1 ] \\ \\ V & = \{ 0 \} \\ \\ \\ \therefore T & \text{ is an empty set} \end{align}

(ii)

\begin{align} \text{No, since } T \text{ is an empty set while } U \text{ contains an element, 1} \end{align}

(iii)

\begin{align} \text{No, since } U \text{ contains the element } 1 \text{ while } V \text{ contains the element } 0 \end{align}

(a)

\begin{align} \text{False, since the set } \{ \text{c, a, r} \} \text{ contains the element c} \end{align}

(b)

\begin{align} \text{False, since the set } \{ \text{c, a, r} \} \text{ does not contain the word 'car'} \end{align}

(c)

\begin{align} \text{False, since } \{ \text{c} \} \text{ is a set and not an element } \end{align}

(d)

\begin{align} \text{False, since } \{ \text{c, a, r} \} \text{ is a set} \end{align}

(a)

\begin{align} X & = \{ x : x \text{ is a prime number} \} \end{align}

(b)

\begin{align} Y & = \{ x: x \text{ is a non-negative multiple of } 4 \} \end{align}

(c)

\begin{align} Z & = \{ x: x \text{ is a factor of 12} \} \end{align}

(a)

\begin{align} \text{False, since the set} \{ 0 \} \text{ contains 1 element, } 0 \end{align}

(b)

\begin{align} \text{True} \end{align}

(c)

\begin{align} \text{False, since the set } \{ \emptyset \} \text{ contains the symbol } \emptyset \end{align}

(d)

\begin{align} \text{True} \end{align}