Question

If A, B and C are three sets and u is the universal set such that n(A) = 200, n(B) = 300 and n(A ⋂ B) = 100. Find (A U B), __________ If A = {1, 2, 3} and B = {3, 4} and C = {1, 3, 5}

Answer 1

Answer:

n(A ∪ B) = 400

Step-by-step explanation:

Given:

n(A) = 200,

n(B) = 300

and n(A ⋂ B) = 100.

Find (A U B):

Formula:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A ∪ B) =   200 + 300 - 100

n(A ∪ B) = 500 - 100

n(A ∪ B) = 400

Answer 2

Answer :

• n(A U B) is 400 .

Step-by-step-Explaination :

Given :-

• If A,B and C are three sets .
• U is the Universal set .
• n(A) = 200 and n(B) = 300 n(A∩B) = 100 .
• A = {1,2,3} and B = {3,4} and C = {1,3,5}.

Find :-

• Find (A∪B) .

How to solve it :

See , here are three sets given A , B and C . Here , Universal set is U .  Then cardinal number of A is given 200 also cardinal number of B is given 300 and also cardinal number of A intersection B is given . Also , What A , B and C sets contain is given . So , it's easy to find (A∪B) . This is from the chapter Sets .

Note :-

Here , the solution is given in the figure :-

Kindly check the attachment

From Here only Extra Finding out :-

So , Let's find out :-

 

$\rm \: A= \{ 1 ,2 ,3\}$

$\rm \: B= \{ 3 ,4\}$

$\rm \: C= \{ 1 ,3 ,5\}$

Now , A∪B means all elements there but no repeatation of same elements

A U B

$\dashrightarrow \bf\{ 1 ,2 ,3 ,4\}$

Hence , 1 , 2 , 3 , 4 are the elements.

More :

• Here , also we can found Intersection of A and B Let's find it out :-

To find out Intersection it means we have to find common of this two elements . So,

A ∩B

$\dashrightarrow \bf\{ 3 \}$

Hence , 3 is the only element intersecting.

Also , we can find out the union of A , B and C .

{A U B U C  }

Same here also Find same elements Between A , B and C but no repeatation.

$\dashrightarrow \bf\{ 1 ,2 ,3 ,4 ,5\}$

Hence , 1 , 2 , 3 , 4 , 5 are the only elements.

Let's find this three Intersection also ,

A ∩B∩ C

This 3 common we have to find :- Remember it can  be a common Between 3 only no 2 common from sets .

$\dashrightarrow \bf\{ 3 \}$

Hence , only 3 is the element that is intersecting.

• Extra formula is given in 2nd attachment kindly check .

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