Which of the following is true?

Options

A. `{2} in {1,2,3}`
B. `phi in {1,2,3}`
C. `{1,2} in {1, {1,2,3}`
D. `0 in {0,1,2}`

Answer

To determine which of the given options is true, we will analyze each option step by step.

### Step 1: Analyze Option 1
**Option 1:** \( \{2\} \in \{1, 2, 3\} \)

- Here, \( \{2\} \) is a set containing the element 2.
- The notation \( \in \) means "is an element of".
- Since \( \{2\} \) is a set and not a single element, it does not belong to the set \( \{1, 2, 3\} \).
- Therefore, **Option 1 is false**.

### Step 2: Analyze Option 2
**Option 2:** \( 5 \in \{1, 2, 3\} \)

- Here, 5 is being considered as an element.
- The set \( \{1, 2, 3\} \) contains the elements 1, 2, and 3, but does not contain 5.
- Therefore, **Option 2 is false**.

### Step 3: Analyze Option 3
**Option 3:** \( \{1, 2\} \in \{1, 2, 3\} \)

- Here, \( \{1, 2\} \) is a set.
- The notation \( \in \) indicates that we are checking if the set \( \{1, 2\} \) is an element of the set \( \{1, 2, 3\} \).
- The set \( \{1, 2, 3\} \) contains the elements 1, 2, and 3, but does not contain the set \( \{1, 2\} \) as an element.
- Therefore, **Option 3 is false**.

### Step 4: Analyze Option 4
**Option 4:** \( 0 \in \{0, 1, 2\} \)

- Here, 0 is being considered as an element.
- The set \( \{0, 1, 2\} \) contains the elements 0, 1, and 2.
- Since 0 is indeed an element of this set, **Option 4 is true**.

### Conclusion
Among the four options, only **Option 4 is true**.

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