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 centimetress tall." true ?

Answer

To determine the conditions under which the statement "Ananya is beautiful and 165 centimetres tall" is true, we can break down the problem step by step.

### Step 1: Define the Statements
Let:
- \( p \): "Ananya is beautiful"
- \( q \): "Ananya is 165 centimetres tall"

### Step 2: Understand the Logical Operation
The statement "Ananya is beautiful and 165 centimetres tall" can be represented as \( p \land q \) (p and q). This means both conditions must be true for the entire statement to be true.

### Step 3: Analyze the Truth Values
To analyze when \( p \land q \) is true, we can create a truth table for the two statements \( p \) and \( q \). The truth table will have the following combinations of truth values:

| \( p \) | \( q \) | \( p \land q \) |
|---------|---------|------------------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

### Step 4: Determine Conditions for Truth
From the truth table:
- The statement \( p \land q \) is true only when both \( p \) and \( q \) are true (i.e., when Ananya is both beautiful and 165 centimetres tall).

### Conclusion
The statement "Ananya is beautiful and 165 centimetres tall" is true if and only if both \( p \) and \( q \) are true. Therefore, the conditions under which the statement is true are:
- Ananya is beautiful (true)
- Ananya is 165 centimetres tall (true)

### Final Answer
The statement is true if both conditions \( p \) and \( q \) are true.

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