Logical reasoning PrepTest 113 · Section 3 · Question 19

Flawed

Sufficient & Necessary Questions / Weaken Questions

Someone sent Drew roses without a card

Sent by someone who knew Drew → Know he likes violets better

~Sent by someone who knew Drew → Included signed card

This argument establishes two facts (Drew received roses; they didn’t have a card) and two conditionals. Those two conditionals do represent all possible sufficient conditions - the person who sent the flowers either did or did not know Drew.

From this, the argument concludes that the florist messed up, because the facts suggest that the person who sent the flowers both knows and doesn’t know Drew. Since that’s logically impossible, it must be the case that there was a mix-up somewhere.

Taking a look at those conditionals, we can see that they are related to the facts that are established. However, only one of them directly overlaps with those facts! The second conditional’s necessary condition definitely didn’t happen here - there was no signed card. That lets us conclude that the flowers were sent by someone who knew Drew (or the florist messed up, which we’ll get back to in a second).

The first conditional’s necessary condition, however, isn’t established as being missing. While Drew did receive roses, that doesn’t mean the person who sent them didn’t know that Drew preferred violets. Maybe they sent him roses because they have a special meaning, or to anger Drew that someone would send him a less preferred flower. In order to get to the conclusion that the florist messed up, we need the premises to establish a logical inconsistency with the action taken. But there isn’t here because the person sending the flowers very well may have intentionally sent roses to Drew despite knowing he likes other flowers better.