Determine whether p,q and "If p, then q " are true or false in each case given below :
1 > 5

Answer

To determine whether the statements p, q, and "If p, then q" are true or false for the case "1 > 5", we will follow these steps:

### Step 1: Define p and q
Let:
- \( p \): "1 > 5"
- \( q \): (We need to define a statement for q, but since the problem does not provide one, we will assume it is arbitrary for this exercise. Let's say \( q \): "Some other statement" which we will evaluate later.)

### Step 2: Evaluate p
We need to determine the truth value of \( p \):
- The statement "1 > 5" is false because 1 is not greater than 5.

Thus, we have:
- \( p \) is **False**.

### Step 3: Evaluate q
Since the problem does not specify what \( q \) is, we cannot evaluate it directly. However, for the sake of this exercise, let's assume \( q \) is also false (as an example).

Thus, we have:
- \( q \) is **False**.

### Step 4: Evaluate "If p, then q"
Now we need to evaluate the implication "If p, then q" (denoted as \( p \rightarrow q \)):
- The truth table for implications states that:
- If \( p \) is true and \( q \) is true, then \( p \rightarrow q \) is true.
- If \( p \) is true and \( q \) is false, then \( p \rightarrow q \) is false.
- If \( p \) is false and \( q \) is true, then \( p \rightarrow q \) is true.
- If both \( p \) and \( q \) are false, then \( p \rightarrow q \) is true.

Since we have:
- \( p \) is **False**
- \( q \) is **False**

According to the truth table, when both \( p \) and \( q \) are false, \( p \rightarrow q \) is **True**.

### Conclusion
In summary:
- \( p \) (1 > 5) is **False**
- \( q \) (arbitrary statement) is **False**
- \( p \rightarrow q \) (If p, then q) is **True**

### Final Result:
- \( p \): False
- \( q \): False
- \( p \rightarrow q \): True

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