Question

A = {x/x is a prime number less than 20} and

B = {y/y is a factor of 20}, then verify the relation

n(A∪B) =n(A) + n(B) - n(A∩B)​

Answer 1

Answer:

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QUESTION :

A = {x/x is a prime number less than 20} and B = {y/y is a factor of 20}, then verify the relationn(A∪B) =n(A) + n(B) - n(A∩B)

SOLUTION :

GIVEN :

➢ A = {x/x is a prime number less than 20}

★ Prime numbers less than 20 are :

• 2,3,5,7,11,13,17,19

⟹ A = { 2,3,5,7,11,13,17,19 }

• n(A) = 8

➢ B = {y/y is a factor of 20}

★ Factors of 20 are :

• 1 × 20

• 2 × 10

• 4 × 5

Therefore, all factors of 20 are 1,2,4,5,10,20

⟹ B = { 1,2,4,5,10,20 }

• n(B) = 6

➙ A∪B = {2,3,5,7,11,13,17,19} ∪ {1,2,4,5,10,20}

➙ A∪B = { 1,2,3,4,5,7,10,11,13,17,19,20 }

• n(A∪B) = 12

➙ A∩B = {2,3,5,7,11,13,17,19}∩{1,2,4,5,10,20}

➙ A∩B = { 2,5 }

• n(A∩B) =2

Now we have,

• n(A) = 8.

• n(B) = 6

• n(A∪B) = 12

• n(A∩B) =2

Given relation...

n(A∪B) =n(A) + n(B) - n(A∩B)

To prove LHS = RHS

LHS = n(A∪B) & RHS = n(A) + n(B) - n(A∩B)

• Substitute the values..

➡ 12 = 8 + 6 - 2

➡ 12 = 14 - 2

➡ 12 = 12

Hence, the relation is verified....

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

A = {x/x is a prime number less than 20} and

B = {y/y is a factor of 20}, then verify the relation

n(A∪B) =n(A) + n(B) - n(A∩B)