# If G is absent whenever F is absent, then F is a sufficient condition for G

True or false and why? I am very confused on this topic: If G is absent whenever F is absent, then F is a sufficient condition for G.

I know that if F is a sufficient condition for G then F guarantees G

Wouldn't this mean that F is not a sufficient condition for G but rather a necessary condition since F needs to be present for G to be present? There by making this statement false?

The short answer is "false". Let's get rid of that confusing wording. All that means is this:

(1) ¬F → ¬G  [ G is absent whenever F is absent ],

(2) F → G   [ F is a sufficient condition for G ].

The converse of (1) is G → F, which informally means that F is a necessary condition for G. That means that neither (1) nor its converse entail (2).

• Too many layers of negation. Is your "false" stating that thing he said was false, is false? or that his assertion that it is false, is false?
– user9166
May 8, 2015 at 0:59
• @jobermark It's the answer to: "True or false and why?" (well, to the first conjunct ;) ) May 8, 2015 at 1:28

No, F being a necessary condition of G simply means that if you have F, G will occur, which is not what you are saying. What you're saying is that G is absent when F is. You are not saying that G is present whenever F is (G can be absent whenever F is but it could also absent on certain occasions when F is present, or during all occasions when F is present). Furthermore, you are not certain that F is the cause for G. Just because two events are temporally contiguous, this does not mean that they are causally related. Unless you establish causality, even if you did establish the fact that G occurs whenever F does, this still does not mean that F necessitates G. There could be other variables that affect both F and G that, when combined in the right manner, produce F without G or vice versa.