Q7 on LR Additional Drills Pg. 16

[sno7]

I don't understand why (A) is the correct answer here.

If, for example, we have 100 kids, and 90 of them want to watch a movie, and the same 90 kids want food, can't it mean that none of the kids who want food want recess?

Why must "not all of the kids who want food want recess" be always true?

[ohthatpatrick]

First, I'll explain why that answer is right, then I'll address your putative counterexample.

Are you already familiar with the Most + Most inference?

When you know that
Most A's are B
and
Most A's are C
then you can infer
Some B's are C

Since we know
most kids want food
and
most kids want movie
then we know
some kids who want food also want the movie

Let's call this kid Billy. Billy wants food and also wants the movie.

We were told that NONE of the kids who want the movie want recess. Since we know Billy wants the movie, we know Billy doesn't want recess.

Billy wants food, wants movie, doesn't want recess.

Proving "Not all A's are B" is as simple as providing AT LEAST ONE example where someone was A, but not B.
To prove "not all kids who want food want recess" means we have AT LEAST ONE example of someone who does want food, but doesn't want recess.

Billy is our example.

As to your scenario ...
If, for example, we have 100 kids, and 90 of them want to watch a movie, and the same 90 kids want food, can't it mean that none of the kids who want food want recess?


You're just getting confused by "not all" and thinking that it means "some are, but some aren't".
It doesn't mean that.
"not all" means "at least one is not".

These are true facts about the world:
- not all humans live on Jupiter
- not all NFL players are female

Remember to prove the first claim, we only need to prove that "at least one human does not live on Jupiter"
and to prove the second, we only need "at least one NFL player is male".

The way we use "not all" conversationally is very different from what it means in a pure logical sense.

Hope this helps.

[sno7]

Thank you!