If p is true,q is also true, then `(p implies q) implies ~| q` is:

Options

A. True
B. p
C. False
D. q

Answer

To solve the problem, we need to evaluate the expression \((p \implies q) \implies \neg q\) given that \(p\) is true and \(q\) is also true. We will break this down step by step.

### Step 1: Understand the Implication
The implication \(p \implies q\) means "if \(p\) is true, then \(q\) is true." This is true if:
- Both \(p\) and \(q\) are true.
- \(p\) is false (regardless of \(q\)).

### Step 2: Evaluate \(p \implies q\)
Since we know that both \(p\) and \(q\) are true:
- \(p = \text{True}\)
- \(q = \text{True}\)

Thus, \(p \implies q\) is:
\[ \text{True} \implies \text{True} = \text{True} \]

### Step 3: Evaluate \(\neg q\)
Now, we need to evaluate \(\neg q\):
- Since \(q\) is true, \(\neg q\) (not \(q\)) is:
\[ \neg \text{True} = \text{False} \]

### Step 4: Evaluate the Entire Expression \((p \implies q) \implies \neg q\)
Now we substitute our results into the expression:
\[ (p \implies q) \implies \neg q = \text{True} \implies \text{False} \]

### Step 5: Determine the Truth Value of the Implication
The implication \(\text{True} \implies \text{False}\) is false. According to the rules of implications:
- An implication is false only when the first part (antecedent) is true and the second part (consequent) is false.

Thus, we conclude:
\[ (p \implies q) \implies \neg q = \text{False} \]

### Final Answer
The truth value of the expression \((p \implies q) \implies \neg q\) is **False**.

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