If x={1,3,5} , y= {1,2,3,} , then `xcap` y is :

Options

A. {1,2,3,4,5}
B. {1,2,3,4,5}
C. [1,3}
D. f.

Answer

To find the intersection of the sets \( x \) and \( y \), we will follow these steps:

### Step 1: Identify the elements in each set.
- Set \( x = \{1, 3, 5\} \)
- Set \( y = \{1, 2, 3\} \)

### Step 2: Determine the common elements between the two sets.
- We need to find elements that are present in both set \( x \) and set \( y \).

### Step 3: Compare the elements.
- The elements in set \( x \) are \( 1, 3, 5 \).
- The elements in set \( y \) are \( 1, 2, 3 \).
- Now, we look for common elements:
- The element \( 1 \) is present in both sets.
- The element \( 3 \) is also present in both sets.
- The element \( 5 \) is not present in set \( y \).
- The element \( 2 \) is not present in set \( x \).

### Step 4: List the common elements.
- The common elements found are \( 1 \) and \( 3 \).

### Step 5: Write the intersection of the two sets.
- Therefore, the intersection of sets \( x \) and \( y \) is:
\[ x \cap y = \{1, 3\} \]

### Final Answer:
\[ x \cap y = \{1, 3\} \]

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