If `A = {1,2,3……..9} , B = {2,4,6,7,8}` and `C = {3,4,5,8,9,10}` then `(A - B) uu C` is .

Options

A. `{1,3,4,5,8,9,10}`
B. `{1,2,3,4,5,6,7,8,9}`
C. `{2,4,6,7,8}`
D. `{1,3,4,5,8,9}`

Answer

To solve the problem, we need to find the result of the expression \( (A - B) \cup C \) where:

- \( A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)
- \( B = \{2, 4, 6, 7, 8\} \)
- \( C = \{3, 4, 5, 8, 9, 10\} \)

### Step 1: Calculate \( A - B \)

The operation \( A - B \) means we need to remove all elements of set \( B \) from set \( A \).

- Elements of \( A \): \( \{1, 2, 3, 4, 5, 6, 7, 8, 9\} \)
- Elements of \( B \): \( \{2, 4, 6, 7, 8\} \)

Now, we will remove the elements of \( B \) from \( A \):

- Remove \( 2 \): Remaining \( \{1, 3, 4, 5, 6, 7, 8, 9\} \)
- Remove \( 4 \): Remaining \( \{1, 3, 5, 6, 7, 8, 9\} \)
- Remove \( 6 \): Remaining \( \{1, 3, 5, 7, 8, 9\} \)
- Remove \( 7 \): Remaining \( \{1, 3, 5, 8, 9\} \)
- Remove \( 8 \): Remaining \( \{1, 3, 5, 9\} \)

Thus, we have:

\[ A - B = \{1, 3, 5, 9\} \]

### Step 2: Calculate \( (A - B) \cup C \)

Now we need to find the union of \( (A - B) \) and \( C \).

- \( A - B = \{1, 3, 5, 9\} \)
- \( C = \{3, 4, 5, 8, 9, 10\} \)

The union operation combines all unique elements from both sets:

- Start with \( \{1, 3, 5, 9\} \)
- Add \( 3 \): Already present
- Add \( 4 \): New element, so now \( \{1, 3, 5, 9, 4\} \)
- Add \( 5 \): Already present
- Add \( 8 \): New element, so now \( \{1, 3, 5, 9, 4, 8\} \)
- Add \( 9 \): Already present
- Add \( 10 \): New element, so now \( \{1, 3, 5, 9, 4, 8, 10\} \)

Thus, the final result is:

\[ (A - B) \cup C = \{1, 3, 4, 5, 8, 9, 10\} \]

### Final Answer

The result of \( (A - B) \cup C \) is:

\[ \{1, 3, 4, 5, 8, 9, 10\} \]

---