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Let a and B Be Two Sets Having 4 and 7 Elements Respectively. Then Write the Maximum Number of Elements that a ∪ B Can Have. - Mathematics

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प्रश्न

Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that \[A \cup B\] can have. 

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उत्तर

\[\text{ We know that }n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ n\left( A \cup B \right) \text{ is maximum when  }n\left( A \cap B \right) \text{ is minimum }\]
\[so, n\left( A \cap B \right) = 0\]
\[\text{ Hence }, n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right) \]
\[ = 4 + 7 - 0\]
\[ = 11\]

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पाठ 1: Sets - Exercise 1.09 [पृष्ठ ४९]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 1 Sets
Exercise 1.09 | Q 7 | पृष्ठ ४९

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