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# diagramming conditional within conditional

Free Trial Member
edited December 2013 14 karma
hi there,

i have a question on diagramming multiple conditionals: e.g., Q#15, section 1 of PT #63 (june 2011), choice B states, "if someone tells the same lie to two different people, then neither of those lied to is owed an apology unless both are." i know this is not the correct answer choice but i had a question as to how we'd diagram a multi-part conditional statement like this. would the correct way be:
someone tells the same lie to two different people --> (at least one owed apology --> both owed apology)? if so, what would be the contrapositive of the entire sentence? i never dealt with a conditional within a conditional so any advice you have would be greatly appreciated!

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• Free Trial Inactive Sage
1878 karma
You got it. The first condition is triggering a second condition. It's good that you placed the second condition in parenthesis as a reminder that the second condition is an independent equation.

The contrapositive would be if you negate the second condition, contradicting the truth of the condition. According to the second condition, if you must apologize to someone, you must apologize to both. If you can prove a situation where you must apologize to someone, but not necessarily both, then it cannot have been an apology for an identical lie told to two people.

If you can contradict the truth of the second condition, then the first condition could not have existed.

I hope I wasn't confusing.
• Free Trial Member
14 karma
thanks so much for the quick reply. let me know if i understood you correctly:

given: "someone tells the same lie to two different people --> (at least one owed apology --> both owed apology)"
contrapositive: someone tells the same lie to two different people --> (both not owed apology --> neither owed apology)

and this is because the negation of a conditional, A --> B is A -->~B, correct?
• Free Trial Inactive Sage
1878 karma
I would phrase the contrapositive by beginning at the opposite end, by negating the second conditional. It would be a bit abstract in this case: If we are discussing a case where you can owe one person, but not both, and apology --> then we cannot be discussing a case where a person said same lie to two people.

It follows the same method as a normal condition:

Normal condition: A --> B
Negation: ~B --> ~A

Double conditional: A --> (C --> D)
Negation: First show we are discussing case where C-->D doesn't apply (i.e. C-->~D or ~D-->C). Once the (C-->D) rule is inapplicable, A must be as well.
14022 karma
Hey guys, sorry to butt in.

There's a lesson on embedded conditionals:
http://7sage.com/lesson/mastery-embedded-conditional

Also a lesson on negating conditionals:

Okay, that's all. Please carry on!
• Member
edited May 2021 1384 karma

So... just to clarify:

If we're starting out with "if someone tells the same lie to two different people, then neither of those lied to is owed an apology unless both are,"

I'd have diagrammed it like this:

Tells same lie to both → (~Both owed apol~1 owed apol and ~2 owed apol)

Getting rid of the embedded conditional (i.e., taking out the parentheses) yields:

Tells same lie to both and ~Both owed apol~1 owed apol and ~2 owed apol

So I get the contrapositive as being:

1 owed apol. or 2 owed apol~Tells same lie to both or Both owed apol

If this looks okay, I guess I'm not sure where negating an 'all statement' (the 2nd referenced video lesson) would come into play?

Could someone help me understand this?