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Concept of sufficient and necessary conditions?
Hey guys,
A 7Sager sent me an email today and I thought you guys could help out! Here it is:
--------------------
I'm preparing to take the LSAT this December so this message is quite urgent.
I've been practicing and I'm feeling confident but I'm having a hard time with the very basic concept of sufficient and necessary conditions. On the surface I understand it but then I read contradictory information.
My question is, well let me use an example.
If I take the LSAT, I must get into Osgoode.
LSAT (sufficient) -->OS (necessary)
Contrapositive
/OS-->/LSAT
If I didn't get into Osgoode I didn't take the LSAT.
-What can I tell you if I got into Osgoode?
-NOTHING because from the necessary condition alone, I could of taken the LSAT or I could of not.
-I get that the occurrence of the necessary condition does not mean the sufficient must also occur, cool.
But I cannot figure out if when:
1. The sufficient condition occurs does the necessary condition have to occur?
2. Can the sufficient condition occur without the necessary condition?
3. What happens when you satisfy the sufficient condition?
For logic games with conditional rules
ex. If F3-->G2
-Let's say "F" is in 4 so I'm correct to say "G" can be anywhere inclucing spot 2?
Please help me clarify.
A 7Sager sent me an email today and I thought you guys could help out! Here it is:
--------------------
I'm preparing to take the LSAT this December so this message is quite urgent.
I've been practicing and I'm feeling confident but I'm having a hard time with the very basic concept of sufficient and necessary conditions. On the surface I understand it but then I read contradictory information.
My question is, well let me use an example.
If I take the LSAT, I must get into Osgoode.
LSAT (sufficient) -->OS (necessary)
Contrapositive
/OS-->/LSAT
If I didn't get into Osgoode I didn't take the LSAT.
-What can I tell you if I got into Osgoode?
-NOTHING because from the necessary condition alone, I could of taken the LSAT or I could of not.
-I get that the occurrence of the necessary condition does not mean the sufficient must also occur, cool.
But I cannot figure out if when:
1. The sufficient condition occurs does the necessary condition have to occur?
2. Can the sufficient condition occur without the necessary condition?
3. What happens when you satisfy the sufficient condition?
For logic games with conditional rules
ex. If F3-->G2
-Let's say "F" is in 4 so I'm correct to say "G" can be anywhere inclucing spot 2?
Please help me clarify.
Comments
From what I can tell I think you understand what sufficient and necessary mean. Below are the answers to the questions you asked.
1. Yes, If sufficient condition occurs the necessary has to occur.
2. No, the sufficient cannot occur without the necessary condition. By its very nature, every time the sufficient condition occurs the necessary has to occur.
3. When you satisfy the sufficient condition, the rule triggers, and the necessary also triggers.
*all three of your questions are basically asking the same thing : )
If F is in 4 or any other place except 3, then the sufficient condition does not get triggered and basically the rule become irrelevant and G is free to be anywhere it wants to be including spot 2.
I hope this helped. Let me know if you have any more questions.
https://7sage.com/lesson/conditional-rules-trigger-v-irrelevant/
2.No
3. The necessary condition is fulfilled.
F/G example: you would be correct in that assertion.
All of this stuff is covered in depth in the core curriculum. My recommendation would be to take some time to get familiar with these concepts, they are extremely important to possess. It would behove you to know these things very well.
I would like to take a second also to give you an example to answer your questions that hopefully is intuitive and "clicks."
If I fight Mike Tyson, I will lose.
That is a statement about events in the world. If next Tuesday you see me and you find out:
1.That I fought Mike Tyson, you have to conclude I lost.
2.if you find out I fought Mike Tyson, our argument doesn't allow us to say that I didn't lose (without the necessary condition.) You can't say "David fought mike Tyson and he didn't lose." That is close to a negation of our statement.
3.You see me and you find out I fought Mike Tyson, (the sufficient is fulfilled) then the necessary is fulfilled: you know I lost.
These three questions are variants of one another.