fameatop wrote:
A sufficient condition can be defined as an event or circumstance whose occurrence indicates that a necessary condition must also occur.
A necessary condition can be defined as an event or circumstance whose occurrence is required in order for a sufficient condition to
Occur.
If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur.
The assumption underlying a conditional statement is that the necessary condition must occur in order for the sufficient condition to occur.
Can somebody explain the meaning of highlighted sentence in the light of 3 statements mentioned above. If possible, kindly explain with proper examples.
Fame
I'm happy to help.
First of all, keep in mind that "necessary & sufficient are complementary conditions -----
If A is necessary for B, then B is sufficient for A.
Let A = the car has gas in its tank
B = one can turn this car on and drive it from place to place
OR
A = polygon is a rectangle
B = polygon is a square
OR
A = I am in California
B = I am in San Francisco, CA
Now, your sentence: "
If a sufficient condition occurs, it means that the necessary condition MUST occur. But if a necessary condition occurs, then it is possible but not certain that the sufficient condition will occur."
If the car moves, then it must have gas. If all you know is that the car has gas, it may or may not turn on (what if the battery is missing?)
If the polygon is square, it is definitely a rectangle as well. If the polygon is a rectangle, then it may or may not be a square.
If I am in SF, I'm definitely in CA, but if I'm in CA, I could be a number of places other than SF ---- LA, San Diego, Lake Tahoe, Yosemite, etc etc.
The terms "necessary" and "sufficient" are alternate ways of phrasing "if-then" statements. The following four statements all say the same thing:
(1) If P, then Q
(2) Only if Q, then P.
(3) P is necessary for Q
(4) Q is sufficient for P
Incidentally, this is why "J if and only if K" is equivalent to "J is necessary and sufficient for K".
Does all this make sense?
Mike
Sorry for digging up such an old thread. I was reading this post and I think there is an error here. From what I understand, If (Sufficient Condition), then (Necessary Condition). Meaning P = Sufficient Condition and Q = Necessary Condition.
Then, shouldn't (3) be Q is necessary for P and (4) P is sufficient for Q. I spent nearly 20 mins trying to understand that and then googled it. Here is what I found on Wikipedia. ""If P then Q", Q is necessary for P, because P cannot be true unless Q is true. Similarly, "P is sufficient for Q" because P being true always implies that Q is true, but P not being true does not always imply that Q is not true." Here is the link to the article:
Let me know if I'm mistaken. Thank you.