Question

please answer it please​

Answer 1

Solution -

As per the diagram shown in the question, we can see that

• A = {1, 2, 3, 4, 5}

•°• Elements of set A are 1, 2, 3, 4 and 5.

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Similarly,

• B = {2, 3, 6, 7, 9}

•°• Elements of set B are 2, 3, 6, 7 and 9.

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Now, we have to prove that

⟹ n(A∪B) + n(A∩B) = n(A) + n(B)

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Firstly, calculate

↣ (A∪B) = {1, 2, 3, 4, 5, 6, 7, 9}

↣ n(A∪B) = 8

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↣ (A∩B) = {2, 3}

↣ n(A∩B) = 2

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↣ A = {1, 2, 3, 4, 5}

↣ n(A) = 5

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↣ B = {2, 3, 6, 7, 9}

↣ n(B) = 5

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Putting all the values

⟹ n(A∪B) + n(A∩B) = n(A) + n(B)

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⟹ 8 + 2 = 5 + 5

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⟹ 10 = 10

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⟹ L.H.S = R.H.S

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★ HENCE PROVED ★