If p, q, r are statement with truth vales F, T, F respectively. Then the truth value of p`rarr`(q`rarr`r) is

Answer

To determine the truth value of the expression \( p \rightarrow (q \rightarrow r) \) where the truth values of \( p, q, r \) are \( F, T, F \) respectively, we can follow these steps:

### Step 1: Identify the truth values
We have:
- \( p = F \) (False)
- \( q = T \) (True)
- \( r = F \) (False)

### Step 2: Evaluate \( q \rightarrow r \)
The implication \( q \rightarrow r \) is evaluated as follows:
- The implication \( A \rightarrow B \) is false only when \( A \) is true and \( B \) is false.
- Here, \( q \) is true (T) and \( r \) is false (F).

Thus, \( q \rightarrow r \) evaluates to:
- Since \( q = T \) and \( r = F \), \( q \rightarrow r = F \).

### Step 3: Evaluate \( p \rightarrow (q \rightarrow r) \)
Now we need to evaluate \( p \rightarrow (q \rightarrow r) \):
- We already found that \( q \rightarrow r = F \).
- Now we have \( p = F \) and \( q \rightarrow r = F \).

Using the implication rule again:
- \( p \rightarrow (q \rightarrow r) \) becomes \( F \rightarrow F \).
- The implication \( F \rightarrow F \) is true (T).

### Conclusion
The truth value of \( p \rightarrow (q \rightarrow r) \) is **True (T)**.

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