If a=phi, b={1,2}, c={-1,-2}, then a×b×c has 4 elements.
Is the statement true or false? Justify your answer.
1
Expert's answer
2019-05-14T09:49:01-0400
By the definition,
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. Products can be specified using set-builder notation, e.g.
A×B={(a,b)∣a∈Aandb∈B}
By the definition,
The cardinality of a set is the number of elements of the set. The cardinality of the output set is equal to the product of the cardinalities of all the input sets. That is,
∣A×B∣=∣A∣⋅∣B∣
Similarly,
∣A×B×C∣=∣A∣⋅∣B∣⋅∣C∣
and so on.
( More information: https://en.wikipedia.org/wiki/Cartesian_product )
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