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 :
`p ^^ s`

Answer

To determine the truth value of the statement \( p \land s \) (read as "p and s"), we will follow these steps:

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

### Step 2: Write down the logical expression
The logical expression we need to evaluate is:
\[ p \land s \]

### Step 3: Substitute the truth values into the expression
Substituting the truth values we have:
- \( p = \text{false} \)
- \( s = \text{true} \)

Thus, the expression becomes:
\[ \text{false} \land \text{true} \]

### Step 4: Evaluate the logical expression
In logical conjunction (AND operation), the result is true only if both operands are true. Here, since \( p \) is false, we have:
\[ \text{false} \land \text{true} = \text{false} \]

### Conclusion
The truth value of the statement \( p \land s \) is **false**.

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