RE: OK Christians. your chance. Convince me of God.
September 21, 2012 at 2:12 pm
(This post was last modified: September 21, 2012 at 2:15 pm by Mystic.)
(September 21, 2012 at 2:03 pm)Rhythm Wrote: Am I mistaken in this, does a premise which contains a necessary condition not have to be expressed as "if and only if", as opposed to sufficient conditions "if"?
I had two classes that I learned logic in, and we never discussed necessary or sufficient conditions. Or if we did, I don't remember.
But "if and only if" is double implication.
It would mean A -> B and B -> A both.
If and only if , would be mean both A and B are sufficient and necessary conditions of each other.
In without double implication.
A -> B
B is a necessary condition for A, but A is not a required for B, rather is proves B if true, while B can be true without A being true.
Quote:If you get an A, you will pass the class - sufficient
If and only if you get an A, you will pass the class - necessary
No, If you get an A, you will pass the class, has both a necessary and sufficient clause.
Getting A is sufficient for passing the class, but passing the class is a necessary requirement for getting an A.
In the case of if and only if, statement, it's double implication.
It means these two sentences both.
IF you get an A, you will pass the class.
If you pass the class, you will get an A.
They are then both sufficient and necessary conditions of each other.
Each has to be true for the other to be true, and if one is true, then the other is true.
