Necessary and Sufficient Condition

• A necessary condition is a condition that must be present for an event to occur.
• A sufficient condition is a condition or set of conditions that will produce the event.

To say that P is necessary for Q is to say that if you don’t have P, you won’t have Q ($Q⟹P$) To say that P is sufficient for Q is to say that if you have P, you will have Q ($P⟹Q$)

A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event.

Realization

If you keep the same two statements and reverse the arrow, necessary and sufficient swap!

For example:

• Being a rectangle is necessary for being a square. If its not a rectangle, it’s not a square
• Being a square is sufficient for being a rectangle. If it’s a square, then it’s a rectangle

"Necessary but not sufficient"

I finally get what this means. Sufficient is stronger than necessary:

• If A is sufficient for B, then A guarantees B
• If A is necessary for B, then you need A for B to happen, But A alone does NOT guarantee B

Related

• Causation