ic Logic

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

Modus Ponens:

Argument in English:
1. If it is raining, then the ground is wet. (p → q)
2. It is raining. (p)

Conclusion: Therefore, the ground is wet. (q)

Argument in Symbolic Form:
1. p → q
2. p
∴ q

Modus Tollens:

Argument in English:
1. If I eat ice cream, then I get a headache. (p → q)
2. I do not have a headache. (¬q)

Conclusion: Therefore, I did not eat ice cream. (¬p)

Argument in Symbolic Form:
1. p → q
2. ¬q
∴ ¬p

Explanation on how to get the symbolic form of each argument:

1. Identify the conditional statement (if-then) and assign sentence letters to the two components.
- In the modus ponens example: "If it is raining, then the ground is wet."
- Assign the letter "p" to "it is raining" and the letter "q" to "the ground is wet."

2. Write the premises and conclusion in symbolic form using the assigned sentence letters.
- The premises become: p → q (conditional statement) and p (given fact).
- The conclusion becomes: q.

3. Repeat steps 1 and 2 for the modus tollens example.
- "If I eat ice cream, then I get a headache."
- Assign the letter "p" to "I eat ice cream" and the letter "q" to "I get a headache."

4. Write the premises and conclusion in symbolic form.
- The premises become: p → q and ¬q (negation of q).
- The conclusion becomes: ¬p.

By following these steps, you can convert arguments stated in English into symbolic form using sentence letters and truth-functional connectives.