Suppose the cardinality of set
A
is 2 and the cardinality of set
B
is 3, what are the cardinalities of the cartesian product
A
×
B
and the power set of
A
×
B
?
6 and 36
5 and 32
6 and 64
5 and 25
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Step-by-step explanation:
The Cartesian product of two sets is the set of all ordered pairs of elements from the two sets. If the cardinality of set A is 2, and the cardinality of set B is 3, then the cardinality of the Cartesian product of A and B is 2 * 3 = 6. This means there are 6 ordered pairs in the set.
The power set of a set is the set of all possible subsets of that set, including the empty set and the set itself. The cardinality of the power set of a set with n elements is 2^n. In this case, the power set of A × B has 2^6 = 64 elements.
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