Rhonda will see the movie tomorrow afternoon only if Paul goes to the concert in the afternoon. Paul will not go to t...

Skylar on February 23, 2020

@hatemz, happy to help!

The first sentence says: "Rhonda will see the movie tomorrow afternoon only if Paul goes to the concert in the afternoon." The term "only if" is a Necessary indicator, so we can make the phrase following it our N condition and the phrase preceding it our S condition.
This gives us: Rhonda will see the movie -> Paul goes to the concert.
We can abbreviate this asL RM -> PC.

The second sentence says "Paul will not go to the concert unless Tedd agrees to go to the concert." The word "unless" introduces the N condition, and the other part of the sentence is negated and made into the S condition.
This gives us: Paul will go to the concert -> Tedd agrees to go to the concert.
We can abbreviate this as: PC -> TC.

We can now combine the abbreviated diagrams we made in the first and second sentences to get the following chain: RM -> PC -> TC.

We can reverse and negate to get the following contrapositive: not TC -> not PC -> not RM.

The third sentence of the passage tells us "Tedd refuses to go to the concert," or "not TC" and makes the conclusion that "Rhonda will not see the movie," or "not RM." This follows the logic of the contrapositive of the chain we made above.

Does that make sense? Please let us know if you have any other questions!