Deardevil wrote:olikatz wrote:On another note, I was wondering if anyone has detailed notes on Conditional Reasoning that they can possibly share with me, or a referral to a page that really sums it up well? As many times as I have re-read those sections in the bibles, I am still confused
I'll try my best to sum it up.
Conditional reasoning revolves around sufficient and necessary conditions.
The former is an occurrence that "guarantees" something that follows,
whether the latter will happen, is happening, or already happened.
For instance, a necessary condition, or a requirement, for the sufficient condition "enter law school" can be "take LSAT."
To be in law school, you must eventually take the LSAT, are currently taking the LSAT, or have already taken the LSAT.
The necessary condition, however, cannot guarantee that the sufficient condition is met.
Just because you have taken the LSAT doesn't necessarily mean you got in law school;
maybe you changed your mind at the last minute or no TT schools accepted you.
Let's denote "enter law school" as "A" and "take LSAT" as "B." As established, it is true that A -> B.
B -> A means "take LSAT" is sufficient for "enter law school," which is not the case. This is commonly known as the mistaken reversal.
Simiarly, another error is to negate both sides, resulting in ~A -> ~B, which says "not entering law school shows that LSAT isn't taken."
Again, that doesn't have to be the case because you not entering could be due to other reasons AFTER taking the LSAT.
Finally, by reversing AND negating, you get the contrapositive, ~B -> ~A, which IS true and is ALWAYS true, given that A -> B is true.
By saying you haven't taken the LSAT, it must mean you aren't going to law school because we know the LSAT is one of the many requirements.
Sufficient conditions can be easily identified by words like "if" and "when."
Anything that sounds remotely like those two indicates sufficiency. Necessity is easily seen with "must" or "required."
Sufficient assumption, or justify the conclusion, questions and assumption questions use these terms,
such as "which one of the following, IF assumed, justifies the conclusion?" or "which assumption below does the author DEPEND/NEED?"
A special case is "only if." Is it sufficient? It has "if..." No. It's actually necessary.
What if I said "you will win only if you train hard?" How would you reword this sentence? "If you win, you MUST train hard."
Finally, there's "unless." At first, this was tricky.
Let's say a problem presents a situation where a person cannot enter a club UNLESS he/she is 21.
There's no "if" or "must." So how do you figure out the sufficient and necessary conditions?
"Unless," or "without," like "only if," modifies what is immediately after it. In this case, it's the age limit.
NOTE that once you determine what is necessary, you have to NEGATE the sufficient condition, the other piece of information.
Translated, this simply reads "if a person CAN enter a club, then he/she must be 21."
Hope this makes sense.
I've never heard of Predictit tbh. 
