Question
Let A = {1, 2} and B = {3, 4}. Write $A \times B$. How many sub sets will $A \times B$ have? List them.

Answer

Here A = {1, 2} and B = {3, 4}
$\therefore A \times B = (1,2) \times (3,4\} $
= {(1, 3}, (1, 4), (2, 3), (2, 4)}
Number of elements in $A \times B = 4$
Number of subsets of $A \times B = {2^4} = 16$
The subset are:
$\phi ,${(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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