Determine whether p,q and "If p, then q " are true or false in each case given below :
5x3=16

Answer

To determine the truth values of \( p \), \( q \), and "If \( p \), then \( q \)" (denoted as \( p \rightarrow q \)), we first need to define what \( p \) and \( q \) represent in the context of the statement given: \( 5 \times 3 = 16 \).

### Step 1: Define \( p \) and \( q \)
Let:
- \( p \): The statement \( 5 \times 3 = 16 \)
- \( q \): A statement that we can define as true or false based on the context. However, since we are only given one equation, we will consider \( q \) as a separate statement that we need to evaluate.

### Step 2: Evaluate \( p \)
We evaluate \( p \):
- \( 5 \times 3 = 15 \), which is not equal to \( 16 \).
- Therefore, \( p \) is **false**.

### Step 3: Evaluate \( q \)
Since \( q \) is not explicitly defined in the problem, we can assume it to be another statement that could be true or false. However, for the sake of this problem, we can assume \( q \) is also false because we are not given a specific statement to evaluate.

### Step 4: Evaluate \( p \rightarrow q \)
The implication \( p \rightarrow q \) (If \( p \), then \( q \)) is evaluated based on the truth values of \( p \) and \( q \):
- The truth table for \( p \rightarrow q \) is as follows:
- If \( p \) is true and \( q \) is true, then \( p \rightarrow q \) is true.
- If \( p \) is true and \( q \) is false, then \( p \rightarrow q \) is false.
- If \( p \) is false and \( q \) is true, then \( p \rightarrow q \) is true.
- If \( p \) is false and \( q \) is false, then \( p \rightarrow q \) is true.

Since we have established that both \( p \) and \( q \) are false:
- \( p \) is false.
- \( q \) is false.
- Therefore, \( p \rightarrow q \) is **true**.

### Summary of Truth Values
- \( p \): False
- \( q \): False
- \( p \rightarrow q \): True

### Final Conclusion
In conclusion, for the statement \( 5 \times 3 = 16 \):
- \( p \) is false.
- \( q \) is false.
- The implication \( p \rightarrow q \) is true.