Q. 83.9( 116 Votes )

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

Answer :

Given: A = {1, 2} and B = {3, 4}

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

Number of elements in (A × B) = 4

n(A × B) = 4

Then number of subsets of set (A × B) = 2n = 24 = 16

number of subsets of set (A × B) = 16

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)}, {(1,4),(2,3),(2,4)}, {(1,3),(2,3), (2,4)}, {(1,3),(1,4),(2,3),(2,4)}.

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