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Senior high school mathematics expert on set problems.
The third power of 3 =27

enumeration method

When a = {1, 2,3}, B= empty set, {1}, {2}, {3}, {1, 2}, {1, 3}, {2,3}.

When A={ 1, 2}, B = {3}, {1, 3}, {2,3}, {1, 2,3} 4.

When A={ 1, 3}, B = {2}, {1, 2}, {2,3}, {1, 2,3} 4.

When a = {2,3}, B = {1}, {1, 2}, {1, 3}, {1, 2,3} 4.

When A={ 1}, b = {2,3}, {1, 2,3} 2.

When A={2}, B={ 1, 3}, {1, 2,3} 2.

When A={3}, B={ 1, 2}, {1, 2,3} 2.

When A= empty set, B={ 1, 2,3}1.

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