William knows the following statement is true: If it rains today, the grass will be wet. Now we’re given a second statement. The grass was wet on Monday. Can you conclude that it rained on Monday?
I want to label our conditional statement, if p then q. So if it rains, p, then q, the grass will be wet. The statement the grass was wet on Monday is a form of q. We know the condition of the grass. Can we take the conclusion q and automatically draw the conditional? If we know q, can we positively say that p is true? If we know the grass is wet, is the only way that happened by rain? No, that’s not true. We cannot take the conclusion of a conditional and draw the if statement from it. So we say no. We cannot conclude that it rained on Monday. Maybe it did. But maybe it didn’t.
Our next option is that it rained on Tuesday. The rain on Tuesday is a p statement. It’s part of our conditional. If we know that it rained on Tuesday, could we conclude that q is true, that the grass would be wet on Tuesday? Yes, we know that it is true. If it rains today, the grass will be wet. That means, we can say with certainty, if it rained on Tuesday, that the grass was wet on Tuesday.