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  4. Let A= 1,2,3,4 . The number of different ordered pairs (B, C) that can be formed such that B ⊆ A , C ⊆ A and B ∩ C is empty, is

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Q. Let $A=\{1,2,3,4\}$. The number of different ordered pairs (B, C) that can be formed such that $B \subseteq A , C \subseteq A$ and $B \cap C$ is empty, is

Permutations and Combinations

Solution:

For each element of set A, there are 3 possibilities i.e.,
(i) element of B but not element of C
(ii) element of C but not element of B
(iii) neither element of B nor element of C
So, number of ways $= 3^4$