for A, it is sufficient that B

P: Tom buys Park Place.

Q: Sally buys hotels for her properties.

S: Sally goes bankrupt.

Y: Sally wins.

I have the following statement:

For Sally to win it is sufficient that she buy hotels for her properties

Now I know that a statement in the form A is sufficient for B means simply A -> B. However, when i translate it into this statement, it doesn't seem to make sense to me. Here is what I think is supposed to be correct according to the definition.

Y -> Q

But this doesn't make sense to me... if it's sufficient that she buys hotels for her properties to win, doesn't that mean that if she buys hotels for her properties, then she wins? so shouldn't it take on the form:

Q -> Y ?

also since it's just sufficient that she buys hotels, doesn't it mean that just because she won, doesn't mean that she bought hotels for her properties, she could have won using some other method right?

I am not sure why you take Y -> Q to mean that Q is sufficient for Y in your question, but that's incorrect.

Sufficient for X means that if the condition (let's say Y) is met, then X will occur whereas necessary means that if X is the case, then Y has occurred.

Thus,

Y -> Q

would mean that Q is necessary for Y. Because this would mean under any scenario where Y obtains, Q also obtains (by modus ponens).

whereas

Q -> Y

would mean that Q is sufficient for Y. Because this would mean that if Q obtains, Y also obtains but that Y might obtain in ways where you Q is not occurring.

• hello i am op and it looks like I didn't pay much attention to the form of the sentence. I see now that the sentence"for Y it is sufficient that Q" translates to "Q is sufficient for Y". Therefore Q -> Y Commented Oct 3, 2015 at 5:07
• @user125535 you should mark this answer as accepted if it helped you.
– user2953
Commented Oct 3, 2015 at 7:19
• @Keelan it doesn't allow me to accept an answer. Only lets me upvote or downvote. I wrote the question as a guest and then registered so that may be a factor. Commented Oct 4, 2015 at 0:19