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For A = {1, 2} and B = {}, determine P(A) P(B)
Chapter 2, Problem 6(choose chapter or problem)
For \(A=\{1,2\}\) and \(B=\{\emptyset\}\), determine \(\mathcal{P}(A) \times \mathcal{P}(B)\).
Questions & Answers
QUESTION:
For \(A=\{1,2\}\) and \(B=\{\emptyset\}\), determine \(\mathcal{P}(A) \times \mathcal{P}(B)\).
ANSWER:Step 1 of 2
A set is a collection of elements. Cartesian product of a set is defined as the ordered pair of elements x and y, where the element x belongs to the first and the element y belongs to the second set.
The power set of a set X is the set of all subsets of the set X. Here, we have to find the power sets of the given set and then the Cartesian product of the sets.
Consider set \(A=\{1,2\}\). The power set of the set A is as follows:
\(\mathcal{P}(A)=\{\emptyset, 1,2,\{1,2\}\}\)
Consider set \(B=\{\emptyset\}\). The power set of the set B is as follows:
\(\mathcal{P}(B)=\{\emptyset,\{\emptyset\}\}\)