Write 'T' for True and 'F' for False.
If `p -= q`, then `p hArr q` will be a tautology.

Answer

To determine whether the statement "If \( p \equiv q \), then \( p \leftrightarrow q \) will be a tautology" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Terms**:
- \( p \equiv q \) means that \( p \) is equivalent to \( q \). This implies that both \( p \) and \( q \) have the same truth value (either both true or both false).
- \( p \leftrightarrow q \) (read as "p if and only if q") is a biconditional statement that is true if both \( p \) and \( q \) are either true or false.

2. **Analyzing the Biconditional**:
- The truth table for \( p \leftrightarrow q \) is as follows:
- If \( p \) is true and \( q \) is true, then \( p \leftrightarrow q \) is true.
- If \( p \) is false and \( q \) is false, then \( p \leftrightarrow q \) is true.
- If \( p \) is true and \( q \) is false, then \( p \leftrightarrow q \) is false.
- If \( p \) is false and \( q \) is true, then \( p \leftrightarrow q \) is false.

3. **Considering the Given Condition**:
- Given that \( p \equiv q \), we know that \( p \) and \( q \) must have the same truth value.
- Therefore, in the cases where \( p \) and \( q \) are both true or both false, \( p \leftrightarrow q \) will always be true.

4. **Conclusion**:
- Since \( p \leftrightarrow q \) is true for all cases where \( p \equiv q \), we conclude that \( p \leftrightarrow q \) is indeed a tautology under the condition that \( p \equiv q \).

5. **Final Answer**:
- Therefore, the statement "If \( p \equiv q \), then \( p \leftrightarrow q \) will be a tautology" is true. We denote this as 'T'.