Which of the following statements are true ?
Every subset of an infinite set is infinite.

Answer

To determine whether the statement "Every subset of an infinite set is infinite" is true or false, we can analyze it step by step.

### Step 1: Understand the Definition of an Infinite Set
An infinite set is a set that has no end; it continues indefinitely. For example, the set of natural numbers \( \{1, 2, 3, \ldots\} \) is an infinite set.

**Hint:** Remember that an infinite set can have an unlimited number of elements.

### Step 2: Consider Subsets of an Infinite Set
A subset is any set that can be formed from the elements of another set. For example, if we take the infinite set of natural numbers \( \{1, 2, 3, \ldots\} \), some of its subsets could be:
- The empty set \( \emptyset \)
- The set of even numbers \( \{2, 4, 6, \ldots\} \)
- The set of odd numbers \( \{1, 3, 5, \ldots\} \)

**Hint:** A subset can have fewer elements than the original set, or it can even have no elements at all.

### Step 3: Identify a Finite Subset
One important subset of any set is the empty set \( \emptyset \). The empty set contains no elements and is considered a finite set.

**Hint:** The empty set is a valid subset of any set, including infinite sets.

### Step 4: Analyze the Statement
The statement claims that every subset of an infinite set is also infinite. However, since we have identified the empty set as a subset of any infinite set, and the empty set is finite, the original statement must be false.

**Hint:** If you can find even one example that contradicts a statement, then that statement is false.

### Conclusion
Thus, the statement "Every subset of an infinite set is infinite" is false because the empty set is a subset of any infinite set and is finite.

**Final Answer:** The statement is false.