If `A={1,2,3}and B={3,5,7}`, the find `A oplusB`.

Answer

To find \( A \oplus B \) (the symmetric difference of sets A and B), we can follow these steps:

### Step 1: Identify the sets
We have:
- Set \( A = \{1, 2, 3\} \)
- Set \( B = \{3, 5, 7\} \)

### Step 2: Find \( A - B \)
To find \( A - B \), we remove the elements of set B from set A.
- Set B contains the element 3, which is also in set A.
- Therefore, we remove 3 from set A.

So,
\[ A - B = \{1, 2\} \]

### Step 3: Find \( B - A \)
Next, we find \( B - A \) by removing the elements of set A from set B.
- Set A contains the element 3, which is also in set B.
- Therefore, we remove 3 from set B.

So,
\[ B - A = \{5, 7\} \]

### Step 4: Find the union of \( (A - B) \) and \( (B - A) \)
Now, we take the union of the two sets we found in steps 2 and 3.
\[ A \oplus B = (A - B) \cup (B - A) = \{1, 2\} \cup \{5, 7\} \]

Combining these sets, we get:
\[ A \oplus B = \{1, 2, 5, 7\} \]

### Final Answer
Thus, the symmetric difference \( A \oplus B \) is:
\[ \{1, 2, 5, 7\} \]

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