Let p be " Ananya is beautiful, " and let q be " Ananya is 165 centimetres tall. "
Under what conditions is the statement, " " Ananya is beautiful and 165 centimetres tall, " false ?

Answer

To determine under what conditions the statement "Ananya is beautiful and 165 centimetres tall" is false, we need to analyze the logical structure of the statement.

1. **Understanding the Statement**: The statement can be represented as \( p \land q \), where:
- \( p \): "Ananya is beautiful"
- \( q \): "Ananya is 165 centimetres tall"

2. **Logical Interpretation**: The conjunction \( p \land q \) (read as "p and q") is true only when both \( p \) and \( q \) are true. The statement \( p \land q \) is false if at least one of the components \( p \) or \( q \) is false.

3. **Conditions for Falsehood**: Therefore, the statement "Ananya is beautiful and 165 centimetres tall" is false under the following conditions:
- If \( p \) is false (Ananya is not beautiful)
- If \( q \) is false (Ananya is not 165 centimetres tall)
- If both \( p \) and \( q \) are false (Ananya is neither beautiful nor 165 centimetres tall)

4. **Conclusion**: The statement \( p \land q \) is false if:
- Ananya is not beautiful (i.e., \( p \) is false)
- Ananya is not 165 centimetres tall (i.e., \( q \) is false)

Thus, the statement "Ananya is beautiful and 165 centimetres tall" is false if either or both of the following conditions hold:
- Ananya is not beautiful.
- Ananya is not 165 centimetres tall.