Question

If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

Answer 1

Dear Student,

◆ Answer -

n(B) = 250

n(U) = 600

● Explanation -

Applying sets formulae,

n(A∪B) = n(A) + n(B) - n(A∩B)

500 = 300 + n(B) - 50

n(B) = 500 - 250

n(B) = 250

Also, to find n(U) -

n(U) = n(B) + n(B)

n(U) = 250 + 350

n(U) = 600

Best luck dear. Hope this helps you...

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1. For two non empty sets A and B

$\sf{n(A \cup \: B) = n(A) + n(B) - n(A \cap B) \: \: }$

2.

$\sf{n( B ') + n(B) = n(U) }$

GIVEN

• n(A) = 300
• n(A∪B) = 500
• n(A∩B) = 50
• n(B′) = 350

TO DETERMINE

• n(B)
• n(U)

CALCULATION

ANSWER TO QUESTION : 1

For two non empty sets A and B

$\sf{n(A \cup \: B) = n(A) + n(B) - n(A \cap B) \: \: }$

$\implies \sf{500= 300+ n(B) - 50 \: \: }$

$\implies \sf{ n(B) = 500 - 300 + 50 \: \: }$

$\implies \sf{ n(B) = 250 \: \: }$

ANSWER TO QUESTION : 2

We know that

$\sf{ n(U) = \: n(B) + n( B ')\: }$

$\implies \sf{ n(U) = \: 250 + 350\: }$

$\implies \sf{ n(U) = \: 600\: }$

RESULT

$1. \: \: \: \: \: \sf{ n(B) = 250 \: \: }$

$2. \: \: \: \: \: \sf{ n(U) = \: 600\: }$

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