मराठी

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:(A ∩ B)' = A' ∪ B' - Mathematics and Statistics

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प्रश्न

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∩ B)' = A' ∪ B'

बेरीज

उत्तर

A = {1, 2, 3, 4}, B = {3, 4, 5, 6},

C = {4, 5, 6, 7, 8}

X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},

A ∩ B = {3, 4}

∴ (A ∩ B)' = {1, 2, 5, 6, 7, 8, 9, 10}   …(i)

A' = {5, 6, 7, 8, 9, 10}

B' = {1, 2, 7, 8, 9, 10}

∴ A' ∪ B' = {1, 2, 5, 6, 7, 8, 9, 10}    ...(ii)

From (i) and (ii), we get

(A ∩ B)' = A' ∪ B'

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Introduction of Set
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पाठ 1: Sets and Relations - Exercise 1.1 [पृष्ठ १०]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board
पाठ 1 Sets and Relations
Exercise 1.1 | Q 5. (iv) | पृष्ठ १०
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