What is the cardinality of these sets in the order of their serial number?
(i){a} (ii){{a}}
(iii){a,{a}} (iv){a,{a},{a,{a}}}
Explanation
(i) {a}
This set contains only the element a.
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Number of elements = 1
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Cardinality = 1
(ii) {{a}}
In this case, the outer curly brackets contain only one thing: the set {a}. Even though {a} has an element inside it, it counts as one single item relative to the outer set.
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Number of elements = 1
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Cardinality = 1
(iii) {a,{a}}
Here, the outer set contains two distinct items separated by a comma:
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The individual element a
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The set {a}
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Number of elements = 2
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Cardinality = 2
(iv) {a,{a},{a,{a}}}
The outer set contains three distinct items separated by commas:
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The element a
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The set {a}
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The set {a,{a}} (this whole group counts as the third item)
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Number of elements = 3
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Cardinality = 3
Final Answer in Order:
The cardinalities are:
1,1,2,3
