Write two arguments in English, one in the form of modus ponens and one in the form of modus tollens. Then, write the arguments in symbols using sentence letters and truth-functional connectives.
The following is one of the arguments and I believe it can be used for both modus ponens and modus tollens depending on how I word it but I don't know how to write it in symbols using sentence letters and truth-functional connectives.
Please help me!!! Thanks
Sure, I can help you with that! Let's start with an example argument in English that can be used for both modus ponens and modus tollens:
Argument:
If it is raining outside (p), then I will take my umbrella (q).
It is raining outside (p).
Now, let's represent this argument in symbols using sentence letters and truth-functional connectives.
Modus Ponens:
p → q
p
∴ q
Modus Tollens:
p → q
~q
∴ ~p
In modus ponens, if we have a conditional statement (p → q) and the antecedent (p) is true, we can affirm the consequent (q) as true.
In modus tollens, if we have a conditional statement (p → q) and the consequent (~q) is false, we can infer the negation of the antecedent (~p) as false.
I hope this helps! Let me know if you have any further questions.