Let p,q,r and s represent simple statements. Assume that p is false, q is true, r is false, and s is true. Determine the truth value of each statement expressed below :
`r ^^ p`

Answer

To determine the truth value of the statement \( r \land p \) (where \( \land \) represents the logical "and"), we will follow these steps:

### Step 1: Identify the truth values of the statements
We are given the following truth values:
- \( p \) is false (F)
- \( r \) is false (F)

### Step 2: Understand the logical "and" operation
The logical "and" operation \( r \land p \) is true only if both \( r \) and \( p \) are true. The truth table for the "and" operation is as follows:

| \( r \) | \( p \) | \( r \land p \) |
|---------|---------|-----------------|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |

### Step 3: Apply the truth values to the logical operation
Since both \( r \) and \( p \) are false:
- \( r = F \)
- \( p = F \)

According to the truth table, when both statements are false, the result of \( r \land p \) is also false.

### Conclusion
Therefore, the truth value of the statement \( r \land p \) is **false**.

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