Let A = { b,d,e,f }, B = { c,d,g,h} and C = {e,f,g,h} .Find :
`( A- B ) uu (B-A) `

Answer

To solve the problem, we need to find the sets \( A - B \) and \( B - A \), and then take the union of these two sets.

### Step 1: Find \( A - B \)
The set \( A - B \) contains all the elements that are in set \( A \) but not in set \( B \).

- Set \( A = \{ b, d, e, f \} \)
- Set \( B = \{ c, d, g, h \} \)

Now, we check each element of \( A \):
- \( b \) is not in \( B \) (include it)
- \( d \) is in \( B \) (do not include it)
- \( e \) is not in \( B \) (include it)
- \( f \) is not in \( B \) (include it)

Thus, \( A - B = \{ b, e, f \} \).

### Step 2: Find \( B - A \)
The set \( B - A \) contains all the elements that are in set \( B \) but not in set \( A \).

- Set \( B = \{ c, d, g, h \} \)
- Set \( A = \{ b, d, e, f \} \)

Now, we check each element of \( B \):
- \( c \) is not in \( A \) (include it)
- \( d \) is in \( A \) (do not include it)
- \( g \) is not in \( A \) (include it)
- \( h \) is not in \( A \) (include it)

Thus, \( B - A = \{ c, g, h \} \).

### Step 3: Find \( (A - B) \cup (B - A) \)
Now we take the union of the two sets we found:

- \( A - B = \{ b, e, f \} \)
- \( B - A = \{ c, g, h \} \)

The union \( (A - B) \cup (B - A) \) contains all the elements that are in either \( A - B \) or \( B - A \).

Combining the elements:
- From \( A - B \): \( b, e, f \)
- From \( B - A \): \( c, g, h \)

Thus, \( (A - B) \cup (B - A) = \{ b, e, f, c, g, h \} \).

### Final Answer
The final result is:
\[ (A - B) \cup (B - A) = \{ b, e, f, c, g, h \} \]

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