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| Definition |
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A group of objects which have the common characteristics and classified in the same group.
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| Describe sets: |
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- Description
- Listing
- Set builder notation
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| Example |
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Describe the multiples of \(3\) which are less than \(19\) by using;
(i) description
(ii) listing
(iii) set builder notation
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(i)
Let the set be represented by \(R\).
Description: \(R\) is the set of multiples of \(3\) which are less than \(19\).
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(ii)
Listing: \(R=\{3, 6, 9, 12, 15, 18\}\)
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(iii)
Set builder notation:
\(R=\{x:x\text{ is the multiple of 3 and }x\lt19\}\)
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| Empty set: |
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| Definition |
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A set that contains no elements.
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- An empty set can be represented with the symbol \(\phi\) or { }.
- An empty set is also called a null set.
- The symbol \(\phi\) is read as phi.
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| The element of a set: |
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| Definition |
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Each object in a set.
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- Each of the elements must satisfy the conditions of the set that is defined.
- Symbol \(\in\) (epsilon) is used to represent ‘is an element of’ the set.
- Symbol \(\notin\) is used to represent ‘is not an element of’ the set.
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| Determine the number of elements of a set: |
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- Number of elements in set \(P\) can be represented by the notation \(n(P)\).
- List all the elements in a set so that the number of elements in the set can be determined.
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| Example |
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Determine the number of elements in the following set.
\(A=\{\text{colours of the traffic light\}}\)
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Noted that
\(\begin{aligned}A&=\{\text{colours of the traffic light\}} \\\\&=\{\text{red, yellow, green\}}. \end{aligned}\)
Thus, \(n(A)=3\).
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| Equality of sets: |
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| Definition |
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Sets in which every element of the sets are the same.
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- If every element in two or more sets are the same, then all the sets are equal.
- The order of elements in a set is not important.
- Symbol \(\neq\) means ‘is not equal to’.
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| Example |
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Determine whether the following pair of sets is an equal set.
\(\begin{aligned}S&=\{\text{letters in the word 'AMAN'}\} \\\\T&=\{\text{letters in the word 'MANA'}\} \end{aligned}\)
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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, \(S=T\).
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