Quick Notes

A group of objects which have the common characteristics and classified in the same group.

Describe the multiples of \(3\) which are less than \(19\) by using;

(i) description

(ii) listing

(iii) set builder notation

(i)

Let the set be represented by \(R\).

Description: \(R\) is the set of multiples of \(3\) which are less than \(19\).

(ii)

Listing: \(R=\{3, 6, 9, 12, 15, 18\}\)

(iii)

Set builder notation:

\(R=\{x:x\text{ is the multiple of 3 and }x\lt19\}\)

A set that contains no elements.

Each object in a set.

Determine the number of elements in the following set.

\(A=\{\text{colours of the traffic light\}}\)

Noted that

\(\begin{aligned}A&=\{\text{colours of the traffic light\}} \\\\&=\{\text{red, yellow, green\}}. \end{aligned}\)

Thus, \(n(A)=3\).

Sets in which every element of the sets are the same.

Determine whether the following pair of sets is an equal set.

\(\begin{aligned}S&=\{\text{letters in the word 'AMAN'}\} \\\\T&=\{\text{letters in the word 'MANA'}\} \end{aligned}\)

We can see that

\(\begin{aligned}S&=\{\text{A, M, A, N}\} \\\\T&=\{\text{M, A, N, A}\}. \end{aligned}\)

Each element in set \(S\) is equal to each element in set \(T\).

Thus, \(S=T\).