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

_________________

Mike McGarry

Magoosh Test Prep