If X= {1,3,5},Y={1,2,3,}, then `XcapY` is :

Options

A. {1,2,3,4,5}
B. {1,2,3,4,5}
C. {1,3}
D. `phi`

Answer

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

### Step 1: Identify the sets
We have two sets:
- \( X = \{1, 3, 5\} \)
- \( Y = \{1, 2, 3\} \)

### Step 2: Understand the concept of intersection
The intersection of two sets, denoted as \( X \cap Y \), consists of all the elements that are common to both sets.

### Step 3: List the elements of each set
- Elements in set \( X \): 1, 3, 5
- Elements in set \( Y \): 1, 2, 3

### Step 4: Find common elements
Now, we will compare the elements in both sets:
- The element **1** is in both \( X \) and \( Y \).
- The element **3** is also in both \( X \) and \( Y \).
- The element **5** is only in \( X \) and not in \( Y \).
- The element **2** is only in \( Y \) and not in \( X \).

### Step 5: Write the intersection
The common elements we found are:
- \( 1 \)
- \( 3 \)

Thus, the intersection \( X \cap Y = \{1, 3\} \).

### Final Answer
The intersection of the sets \( X \) and \( Y \) is:
\[ X \cap Y = \{1, 3\} \]

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