self doubt

Question

how to check the validity of an a argument using laws of logics

Answer 1

 Step 1: Identify the Premises and Conclusion
$Premises$:
\[1. \text{ } P \rightarrow Q\]
\[2. \text{ } P\]

$Conclusion$:
\[3. \text{ } Q\]

Step 2: Translate into Symbolic Form:
\[1. \text{ } P \rightarrow Q\]
\[2. \text{ } P\]
\[ \therefore \text{ } Q\]

Step 3: Apply Logical Rules:
- We'll use the law of modus ponens:
\[\frac{P \rightarrow Q \text{ and } P}{\therefore Q}\]

Step 4: Evaluate Validity:
- By modus ponens, from premises 1 and 2, we can deduce the conclusion (Q). Therefore, the argument is valid because the conclusion logically follows from the premises.