Question

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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given :-

A = { x €R , 0< x< 3 }

B = { x€R, 1≤x≤5}

To find:-

Find A ∆ B ?

Solution :-

Method -1:-

Given sets are :

A = { x €R , 0< x< 3 }

=> A = { 1,2}

B = { x€R, 1≤x≤5}

=> B = { 1,2,3,4,5}

We know that

A∆B = (A-B) U (B-A)

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

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

Now

(A-B) U ( B-A)

=> { } U { 3,4,5}

=> { 3,4,5}

Therefore, (A-B) U ( B-A) = { 3,4,5}

Method -2:-

A = { 1,2}

B = {1,2,3,4,5}

We know that

A∆B = (AUB)-(AnB)

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

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

Now,

(AUB)-(AnB)

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

=> {3,4,5}

Therefore, (A-B) U ( B-A) = { 3,4,5}

Answer:-

A∆B for the given problem is { 3,4,5}

Used formulae:-

• A∆B is the symmetric difference of the two sets A and B

• A∆B = (A-B) U (B-A)

• A∆B = (AUB)-(AnB)

• AUB is the set of all elements in either A or in B or in both.

• AnB is the set of all common elements in both A and B.

• A-B is the set of elements in only A

• B-A is the set of elements in only B