Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. "
Under what cooditions is the statement," Ananya is beauiful or 165 centimetres tall, " true?

Answer

To determine the conditions under which the statement "Ananya is beautiful or 165 centimetres tall" is true, we can analyze the logical expression using the variables defined:

Let:
- \( P \): "Ananya is beautiful"
- \( Q \): "Ananya is 165 centimetres tall"

The statement can be expressed as \( P \lor Q \) (P or Q).

### Step-by-Step Solution:

1. **Understanding the Logical OR**:
The logical OR operator (\( \lor \)) means that the statement \( P \lor Q \) is true if at least one of the statements \( P \) or \( Q \) is true.

2. **Constructing the Truth Table**:
We will create a truth table to analyze all possible truth values for \( P \) and \( Q \):

| \( P \) (Ananya is beautiful) | \( Q \) (Ananya is 165 cm tall) | \( P \lor Q \) |
|-------------------------------|---------------------------------|----------------|
| True | True | True |
| True | False | True |
| False | True | True |
| False | False | False |

3. **Analyzing the Truth Table**:
- The statement \( P \lor Q \) is true in the following cases:
- When both \( P \) and \( Q \) are true.
- When \( P \) is true and \( Q \) is false.
- When \( P \) is false and \( Q \) is true.
- The statement \( P \lor Q \) is false only when both \( P \) and \( Q \) are false.

4. **Conclusion**:
Therefore, the statement "Ananya is beautiful or 165 centimetres tall" is true under the following conditions:
- Ananya is beautiful (P is true).
- Ananya is 165 centimetres tall (Q is true).
- Both statements can be true at the same time.

### Final Answer:
The statement "Ananya is beautiful or 165 centimetres tall" is true if at least one of the statements \( P \) or \( Q \) is true.

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