Question

If A={1, 2,3,4,5} B={2, 3,4,7} then A∆B

Answer 1

Step-by-step explanation:

Given :-

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

B={2, 3,4,7}

To find :-

Find A ∆ B ?

Solution :-

Method -1:-

Given sets are :

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

B={2, 3,4,7}

We know that

A ∆ B = (A-B) U (B-A)

A - B = { 1,2,3,4,5} - { 2,3,4,7}

=> A - B = { 1,5}

B- A = { 2,3,4,7} -{1,2,3,4,5}

=> B- A = {7}

Now A∆B = (A-B) U (B-A)

=> A∆B = {1,5} U { 7}

=> A∆B = {1,5,7}

Method -2:-

Given sets are :

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

B={2, 3,4,7}

We know that

A ∆ B = (AUB ) - (AnB)

AUB = { 1,2,3,4,5} U { 2,3,4,7}

=> AUB ={ 1,2,3,4,5,7}

AnB = { 1,2,3,4,5} n { 2,3,4,7}

=> AnB = { 2,3,4}

Now ,

A∆B = (AUB ) - (AnB)

=> A∆B = { 1,2,3,4,5,7} -{2,3,4}

=> A∆B = {1,5,7}

Answer :-

A∆B = {1,5,7} for the given problem

Used formulae:-

• A ∆ B = (AUB ) - (AnB)

• A∆B = (A-B) U (B-A)

• The symmetric difference between two sets A and B is denoted by A∆B