Question

Find the symmetric difference of\(A = \left\{ {1,3,5} \right\}\)and\(B = \left\{ {1,2,3} \right\}\).

Short answer

Thus, the symmetric difference is\(\left\{ {2,5} \right\}\).

Step-by-step solution

Given

Given in the question,

\(A = \left\{ {1,3,5} \right\}\)and \(B = \left\{ {1,2,3} \right\}\) .

We need to solve the symmetric difference.

concept 

Symmetric difference between A and B, a set that contains an element in A or B, but not in both A and B.

calculation 

Here we find the symmetric difference of \(A = \left\{ {1,3,5} \right\}\)and\(B = \left\{ {1,2,3} \right\}\).

Now we know the formula of symmetric difference .

\(A \oplus B = \left( {A \cup B} \right) - \left( {A \cap B} \right)\)___________(1)

Here we find \(A \cup B\).

\(A \cup B = \left\{ {1,2,3,5} \right\}\)

And also find \(A \cap B\).

\(A \cap B = \left\{ {1,3} \right\}\)

Put the value in equation (1)

\(\left( {A \cup B} \right) - \left( {A \cap B} \right) = \left\{ {1,2,3,5} \right\} - \left\{ {1,3} \right\}\)

= \(\left\{ {2,5} \right\}\)

Then we get,

\(A \oplus B = \left\{ {2,5} \right\}\).

Hence, the symmetric difference is\(\left\{ {2,5} \right\}\).