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 :
`q ^^ r`

Answer

To determine the truth value of the statement \( q \land r \) (which is read as "q and r"), we can follow these steps:

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

### Step 2: Write down the truth values for \( q \) and \( r \)
From the information provided:
- \( q = \text{true} \) (T)
- \( r = \text{false} \) (F)

### Step 3: Apply the AND operation
The AND operation (denoted by \( \land \)) requires both operands to be true for the result to be true. The truth table for the AND operation is as follows:
- T AND T = T
- T AND F = F
- F AND T = F
- F AND F = F

### Step 4: Evaluate \( q \land r \)
Now we substitute the truth values into the expression \( q \land r \):
- \( q \land r = \text{true} \land \text{false} \)

According to the truth table:
- T AND F = F

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

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