Which of the following is a true statement ?

Options

A. `{a}in{a,b,c}`
B. `{a}sub{a,b,c}`
C. `phiin{a,b,c}`
D. None of these

Answer

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

### Step 1: Analyze Option 1
**Statement:** \( a \in \{a, b, c\} \)

- Here, the statement claims that \( a \) is an element of the set \( \{a, b, c\} \).
- This statement is true because \( a \) is indeed one of the elements in the set \( \{a, b, c\} \).

### Step 2: Analyze Option 2
**Statement:** \( \{a\} \subseteq \{a, b, c\} \)

- This statement claims that the set containing \( a \) is a subset of the set \( \{a, b, c\} \).
- A set \( A \) is a subset of set \( B \) if every element of \( A \) is also an element of \( B \).
- Since \( a \) is an element of \( \{a, b, c\} \), the set \( \{a\} \) is indeed a subset of \( \{a, b, c\} \).
- Therefore, this statement is true.

### Step 3: Analyze Option 3
**Statement:** \( \emptyset \in \{a, b, c\} \)

- This statement claims that the empty set \( \emptyset \) is an element of the set \( \{a, b, c\} \).
- The empty set is not an element of \( \{a, b, c\} \) because \( \{a, b, c\} \) contains only the elements \( a, b, \) and \( c \).
- Therefore, this statement is false.

### Step 4: Analyze Option 4
**Statement:** \( \emptyset \subseteq \{a, b, c\} \)

- This statement claims that the empty set is a subset of \( \{a, b, c\} \).
- The empty set is a subset of every set, including \( \{a, b, c\} \).
- Therefore, this statement is true.

### Conclusion
From the analysis:
- Option 1 is true.
- Option 2 is true.
- Option 3 is false.
- Option 4 is true.

Thus, the true statements are Option 1, Option 2, and Option 4.