Hi everyone,

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!):