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Proving Formula for nAUB Video Lecture | Additional Study Material for Class 11

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FAQs on Proving Formula for nAUB Video Lecture - Additional Study Material for Class 11

1. What is the formula for n(A U B)?
Ans. The formula for n(A U B) is given by n(A) + n(B) - n(A ∩ B), where n(A) represents the number of elements in set A, n(B) represents the number of elements in set B, and n(A ∩ B) represents the number of elements common to both sets A and B.
2. How can I prove the formula for n(A U B)?
Ans. To prove the formula for n(A U B), you can use the concept of Venn diagrams. Draw two overlapping circles representing sets A and B. Count the number of elements in each set separately and then count the number of elements common to both sets. Finally, add the number of elements in A, the number of elements in B, and subtract the number of common elements. This will give you the total number of elements in the union of sets A and B.
3. Can you provide an example to understand the formula for n(A U B)?
Ans. Sure! Let's consider two sets, A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. To find n(A U B), we count the number of elements in each set separately. n(A) = 4 and n(B) = 4. Now, we find the number of elements common to both sets, which is n(A ∩ B) = 2 (as 3 and 4 are common). Using the formula, n(A U B) = n(A) + n(B) - n(A ∩ B) = 4 + 4 - 2 = 6. Therefore, the union of sets A and B contains 6 elements.
4. Is the formula for n(A U B) applicable for any two sets?
Ans. Yes, the formula for n(A U B) is applicable for any two sets. It is a general formula that provides the number of elements in the union of two sets. Whether the sets contain numbers, objects, or any other type of elements, the formula remains the same. It calculates the total number of distinct elements present in both sets, considering any common elements only once.
5. Can the formula for n(A U B) be extended to more than two sets?
Ans. Yes, the formula for n(A U B) can be extended to more than two sets. For three sets A, B, and C, the formula becomes n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C). Similarly, for four sets, the formula becomes more complex. However, the basic principle remains the same – count the number of elements in each set separately, consider common elements only once, and calculate the total number of distinct elements in the union of all sets.
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