Question

if A={1,5,7,9,10} B=1,5,8} find A∆B​

Answer 1

{2,4,6,8,10}

A={2,4,6,8,10}

B={1,3,5,7,9}

A−B={2,4,6,8,10}−{1,3,5,7,9}={2,4,6,8,10}

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

A={1,5,7,9,10}

B=1,5,8}

To find :-

Find A∆B ?

Solution :-

Method -1:-

Given sets are :

A={1,5,7,9,10}

B={1,5,8}

We know that

A ∆ B = (AUB) - (AnB)

AUB = {1,5,7,9,10} U { 1,5,8}

AUB = { 1,5,7,8,9,10}

and

AnB = {1,5,7,9,10} n { 1,5,8}

=> AnB = { 1,5}

Now,

A∆B = (AUB) - (AnB)

=> A∆B = { 1,5,7,8,9,10} - {1,5}

=> A∆B = { 7,8,9,10}

Method -2:-

Given sets are :

A={1,5,7,9,10}

B={1,5,8}

We know that

A∆B = (A-B) U (B-A)

A-B = {1,5,7,9,10} - { 1,5,8}

=> A-B = { 7,9,10}

B-A = { 1,5,8} - {1,5,7,9,10}

=> B-A = { 8}

Now,

A∆B = (A-B) U (B-A)

=> A∆B = {7,9,10}U { 8}

=> A∆B = { 7,8,9,10}

Answer:-

A∆B for the given problem is { 7,8,9,10}

Used formulae:-

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

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

→ A∆B is the symmetric difference between A and B