Question

If A and B are two sets such that AUB has 18 elements. A has 8 elements and B has 15 elements,how many elements does A union B have

Answer 1

Step-by-step explanation:

As

n(A u B)= n(a) + n(b) -n(a intersection b)

18 = 8 + 15 - n(a intersection b)

n(a intersection b) = 5

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Answer 2

Given:

→ If A and B are two sets such that A U B has 18 elements.

→ A has 8 elements and B has 15 elements.

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To find:

→ How many elements does A U B have.

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We know that,

→ A U B = 18.

→ A = 8.

→ B = 15.

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Using formula:

★ n (A U B) = n (A) + n (B) - n (A ∩ B)

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Calculations:

→ 18 = 8 + 15 - n (A ∩ B)

→ 18 = 23 - n (A ∩ B)

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Taking 23 to the other side: [Remember to change signs when moving LHS to RHS/RHS to LHS].

→ 18 - 23 = - n (A ∩ B)

→ - 5 = - n (A ∩ B)

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Cancelling -5 and -n we get positive value:

→ n = 5

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Therefore, A ∩ B = 5 elements.