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Question

Let A={1,2} and B={3,4}. Write A×B and find how many subsets will A×B have? List them.

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Solution

A={1,2} and B={3,4}
A×B={(1,3),(1,4),(2,3),(2,4)}
n(A×B)=4

We know that if n(A×B)=r
Then, number of subsets of A×B is 2r
Therefore the set A×B has 24 = 16 subsets.
These are
ϕ{(1,3)},{(1,4)},{(2,3)},{(2,4)},{(1,3),(1,4)},{(1,3),(2,3)},{(1,3),(2,4)},
{(1,4),(2,3)},{(1,4),(2,4)},{(2,3),(2,4)},{(1,3),(1,4),(2,3)},{(1,3),(1,4),(2,4)},
{(1,3),(2,3),(2,4)},{(1,4),(2,3),(2,4)},{(1,3),(1,4),(2,3),(2,4)}}

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