# Modus Ponens or Modus Tollens

• Mar 24th 2013, 01:18 PM
rhymin
Modus Ponens or Modus Tollens
I am confused by these. Here is the problem:

For each of the following pairs of statements, use Modus Ponens or Modus Tollens to fill in the blank line so that a valid argument is presented.

a) If Janice has trouble starting her car, then her daughter Angela will check Janice's spark plus.
Janice had trouble starting her car.
∴ ___________________________________

b) If Brady solved the first problem correctly, then the answer he obtained is 137.
∴ ___________________________________

c) If this is a repeat-until loop, then the body of this loop is executed at least once.
_____________________________________
∴ The body of the loop is executed at least once.

d) If Tim plays basketball in the afternoon, then he will not watch television in the evening.
_____________________________________
∴ Tim didn't play basketball in the afternoon.

Here is what I have:
a) Her daughter Angelawill check Janice's spark plugs
b) Brady did not solve the problem correctly
c) This is a repeat-until loop
d) Tim watched television in the evening

I'm just not sure how to write these using Modus Ponens or Modus Tollens. Confusing.
• Mar 24th 2013, 01:28 PM
Plato
Re: Modus Ponens or Modus Tollens
Quote:

Originally Posted by rhymin
For each of the following pairs of statements, use Modus Ponens or Modus Tollens to fill in the blank line so that a valid argument is presented.

a) If Janice has trouble starting her car, then her daughter Angela will check Janice's spark plus.
Janice had trouble starting her car.
∴ ___________________________________

b) If Brady solved the first problem correctly, then the answer he obtained is 137.
∴ ___________________________________

c) If this is a repeat-until loop, then the body of this loop is executed at least once.
_____________________________________
∴ The body of the loop is executed at least once.

d) If Tim plays basketball in the afternoon, then he will not watch television in the evening.
_____________________________________
∴ Tim didn't play basketball in the afternoon.

Here is what I have:
a) Her daughter Angelawill check Janice's spark plugs
b) Brady did not solve the problem correctly
c) This is a repeat-until loop
d) Tim watched television in the evening

I'm just not sure how to write these using Modus Ponens or Modus Tollens. Confusing.

I am really confused too. Are you saying that you don't know which is which?
You have the correct answers for the 'blanks'. So what is your question?
• Mar 24th 2013, 01:35 PM
rhymin
Re: Modus Ponens or Modus Tollens
Well the textbook said to use Modus Ponens or Modus Tollens to fill in the blank, which should look something like this:

[p ^ (p → q)] → q

or

p → q
¬q
______
∴¬p

But, I'm not quite sure how exactly to write these out.
• Mar 24th 2013, 01:43 PM
Plato
Re: Modus Ponens or Modus Tollens
Quote:

Originally Posted by rhymin
Well the textbook said to use Modus Ponens or Modus Tollens to fill in the blank, which should look something like this:

[p ^ (p → q)] → q

or

p → q
¬q
______
∴¬p

But, I'm not quite sure how exactly to write these out.

I really think that you are over-thinking this question.
As far as I am concerned, I taught this for over forty years, you have completed the question correctly.
You have correctly applied the rules.

Now, I am not your instructor. So I cannot be sure what you mean,
• Mar 24th 2013, 01:47 PM
rhymin
Re: Modus Ponens or Modus Tollens
Okay thank you. I guess I was over thinking it. I just got confused because the examples go very in depth with the "p, q, ∴, →, ¬, etc." symbols and letters and it is very hard for me to follow.