# Symbolic Logic

Prove the following argument:

It is false that both Arthur is not anxious and Billy is not boisterous

If Xavier is difficult and Billy is boisterous then Penelope is a prude

If Xavier is not difficult then Arthur is anxious

Arthur is not anxious

Therefore, it is false that if Xavier is difficult then Penelope is not a prude.

https://brainmass.com/philosophy/logic-critical-thinking/symbolic-logic-125762

#### Solution Preview

Please see attached file.

1. It is false that both Arthur is not anxious and Billy is not boisterous.

2. If Xavier is difficult and Billy is boisterous then Penelope is a prude.

3. If Xavier is not difficult then Arthur is anxious.

4. Arthur is not anxious.

5. Therefore, it is false that if Xavier is difficult then Penelope is not a prude.

Before you can construct a proof for an argument like the one above, you need first to translate it into your symbolic language. Once you have done this, you can then construct a proof using the rules of inference that you should have learned in your class.

To translate this argument into symbols, first you need to identify all of the simple propositions that occur in the argument; then you need to assign a symbol ...

#### Solution Summary

Symbolic Logic is considered.