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  4. Let A = 1, 2, 3, 4, B = 2, 4, 6. Then the number of sets C such that A∩ B⊆ C⊆ A∪ B is:

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Q. Let A = {1, 2, 3, 4}, B = {2, 4, 6}. Then the number of sets C such that $ A\cap B\subseteq C\subseteq A\cup B $ is:

KEAMKEAM 2006

Solution:

$ A\cap B=\{2,4\} $ $ \{A\cap B\}\subseteq \{1,2,4\},\{3,2,4\}, $ $ \{6,2,4\},\{1,3,2,4\} $ $ \{1,3,6,2,4\}\subseteq A\cup B $ $ \Rightarrow $ $ n(C)=8 $