1.Set Theory
medium

If $U =\{1,2,3,4,5,6,7,8,9\}, A =\{2,4,6,8\}$ and $B =\{2,3,5,7\} .$ Verify that

$(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$

Option A
Option B
Option C
Option D

Solution

$U=\{1,2,3,4,5,6,7,8,9\}$

$A=\{2,4,6,8\}, B=\{2,3,5,7\}$

$(A \cap B)^{\prime}=\{2\}^{\prime}=\{1,3,4,5,6,7,8,9\}$

$A^{\prime} \cup B^{\prime}=\{1,3,5,7,9\} \cup\{1,4,6,8,9\}=\{1,3,4,5,6,7,8,9\}$

$\therefore(A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}$

Standard 11
Mathematics

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