Hi Jim,

Can you use simplification in this way?

(P • Q) ⊃ R

Therefore P ⊃ R

In other words can you simplify the statement P and Q even though it is the antecedent to the conditional?

Thank you!!!!

**It is generally improper to simplify a conjunction within parentheses (that is, within a more compound proposition). This is simply because such a “simplification” is often invalid, as in your example.**

**One way to check is to remember that a proper rule of inference will always produce a valid implication. So if you can show that performing the operation is not valid, then it is improper.**

**In your example, we can check implication by using a shorter truth table, making the first proposition true and the second false, as follows:**

**(P • Q) ⊃ R ∴ P ⊃ R**

** T F**

**Starting with the false second conditional, you can complete the truth table with P as True, Q as False, and R as False. These truth values make the first proposition true and the second false. This means that the first does not imply the second, which shows that the simplification is not valid.**

**Blessings!**