Question

if A={ 1,2,3,4};B{3,4,5,6} then find n(A∆B)
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Answer 1

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solution

A={ 1,2,3,4};B{3,4,5,6}

n(A∩B)={3,4}

n(AUB)={1,2,3,4,5,6}

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I hope it helps

Answer 2

Step-by-step explanation:

Given :-

A = { 1,2,3,4};

B = {3,4,5,6}

To Find :-

Find n(A∆B) ?

Solution :-

Method-1:-

Given sets are :

A = { 1,2,3,4};

B = {3,4,5,6}

We know that

A∆B = (AUB)-(AnB)

AUB = { 1,2,3,4} U { 3,4,5,6}

=> AUB = { 1,2,3,4,5,6 }

AnB = { 1,2,3,4} n { 3,4,5,6}

=> AnB = { 3,4}

Now,(AUB)-(AnB)

=> { 1,2,3,4,5,6 } - { 3,4}

=> { 1,2,5,6}

Therefore, A∆B = { 1,2,5,6}

The elements in A∆B = 4

Therefore, n(A∆B) = 4

Method-2:-

Given sets are :

A = { 1,2,3,4};

B = {3,4,5,6}

We know that

A∆B = (A-B) U (B-A)

A-B = { 1,2,3,4} - { 3,4,5,6}

=> A-B = { 1,2}

and

B-A = { 3,4,5,6} - { 1,2,3,4}

=> B-A = { 5,6}

Now,

(A-B) U (B-A)

=> { 1,2} U { 5,6}

=> (A-B) U (B-A) = { 1,2,5,6}

Therefore, A∆B = { 1,2,5,6}

The elements in A∆B = 4

Therefore, n(A∆B) = 4

Answer :-

The value of n(A∆B) for the given problem is 4

Used Formulae:-

→ A∆B = (AUB)-(AnB)

→ A∆B = (A-B) U (B-A)