I’m writing to follow up on a discussion we had in class today, regarding methods for translating conditional (“if…then”) statements from English to symbols.
We started with:
If it rained, the ground got wet.
Which we symbolized as
R -> W
Where R = “it rained” and W = “the ground got wet”.
We then got stuck on the phrase:
It rained only if the ground got wet.
The correct symbolic version of this is:
R -> W
just as it appeared in the slides, where R = “it rained” and W = “the ground got wet”, just as before. This is counterintuitive, but true!
For a longer discussion, with some better examples, take a look at this page (otherwise, just memorize it!):