Most people who are skilled banjo players are also skilled guitar players. But most people who are skilled guitar pla...

rpark on January 10, 2020

please explain

are we able to diagram this

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SamA on January 11, 2020

Hello @rpark,

It is possible to diagram quantifiers if it helps you understand the question. You could even draw up something like a Venn diagram to demonstrate these relationships. I'll show you the logic as it would be represented in our quantifiers lesson.
Skilled banjo player = SBP
Skilled guitar player = SGP

From our first premise, we have:
SBP - - - most - - - - SGP
What can we conclude from this?
SGP - - - some - - - - SBP

So we have this group of some people who are skilled with both a guitar and a banjo. Most skilled banjo players belong to this group.

Then we are given our second premise.
SGP - - - - - most - - - - - - not SBP

Our group of people who play both instruments makes up a majority of banjo players, but a minority of guitar players. What can we conclude from this?

Sometimes, it helps to plug in some real numbers until you are comfortable with this type of reasoning. Let's say there are 20 people who play both instruments

Both: 20

Let's say there are 30 total banjo players. That is consistent with our first premise, because 2/3 would also play guitar.

Banjo Players: 30

In order for this "both" group to be a minority of guitar players, we would need more than 40 guitar players.

Guitar Players: 41+

Because our group of "both" is constant, we must conclude that the guitar group is bigger than the banjo group.