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) = 2^{n} = 2^{4} = 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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PREVIOUSLet A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
(i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.NEXTLet A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

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