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1. PT 19 S2 Q19:
there is no reason not to try my herb juice.
how is this different from "you should try my herb juice."

2. negate "most of these apples are rotten"
i got "some of the apples are not rotten"
but the answer key says: "at least half of these apples are not rotten"
how did they arrive at that answer?

3. Negate "it is unlikely that Simone will come"
i got "it is likely that Simone will come"
but the answer key says: "it is not unlikely that Simone will come".
How are they different?

gg2 wrote:1. PT 19 S2 Q19:
there is no reason not to try my herb juice.
how is this different from "you should try my herb juice."

You're doing too much here. If I were to say that there's no reason not to exercise an option, that doesn't mean that you should exercise it. It just means there's not any reasons to not exercise it. You can't take the lack of reasons against an action to infer a reason for the action.

gg2 wrote:2. negate "most of these apples are rotten"
i got "some of the apples are not rotten"
but the answer key says: "at least half of these apples are not rotten"
how did they arrive at that answer?

Most of these apples are not rotten. Meaning that a majority are not rotten. Thus, at least half are not rotten.

gg2 wrote:3. Negate "it is unlikely that Simone will come"
i got "it is likely that Simone will come"
but the answer key says: "it is not unlikely that Simone will come".
How are they different?

It is not unlikely that Simone will come.

The summary here is that when you are negating a phrase, you simply deny the presence of the relevant action, usually by adding not. You don't take the opposite of the relevant action. For example, the sky will be dark tomorrow. If we negate this then we have: the sky will not be dark tomorrow. Not the sky will be light tomorrow. See the difference?

gg2 wrote:1. PT 19 S2 Q19:
there is no reason not to try my herb juice.
how is this different from "you should try my herb juice."

If you say someone should try your herb juice, there exists a reason why they should try it. For example, it's going to give them really shiny hair. If you say there's no reason *not* to try it, it just means that there is no reason against trying it, but not necessarily a reason why one *should* try it. So if I just say "there's no reason not to try it", I'm basically saying something like, "It's not going to do anything bad if you do try it."

Does that make sense? It's the difference between your friend encouraging you to try a new kind of root beer when you're deciding what soda to buy, because they know you like root beer ("You should try it! You have a reason to, because it's your favorite kind of soda and you might discover a new favorite brand if you try it."), and a friend saying you might as well try a new kind of root beer, because you don't have any reason not to, while not necessarily actively encouraging you to try it ("You don't have any reason not to try a new root beer. Do what you want though.").

Daily_Double wrote:

gg2 wrote:1. PT 19 S2 Q19:
there is no reason not to try my herb juice.
how is this different from "you should try my herb juice."

You're doing too much here. If I were to say that there's no reason not to exercise an option, that doesn't mean that you should exercise it. It just means there's not any reasons to not exercise it. You can't take the lack of reasons against an action to infer a reason for the action.

gg2 wrote:2. negate "most of these apples are rotten"
i got "some of the apples are not rotten"
but the answer key says: "at least half of these apples are not rotten"
how did they arrive at that answer?

Most of these apples are not rotten. Meaning that a majority are not rotten. Thus, at least half are not rotten.

gg2 wrote:3. Negate "it is unlikely that Simone will come"
i got "it is likely that Simone will come"
but the answer key says: "it is not unlikely that Simone will come".
How are they different?

It is not unlikely that Simone will come.

The summary here is that when you are negating a phrase, you simply deny the presence of the relevant action, usually by adding not. You don't take the opposite of the relevant action. For example, the sky will be dark tomorrow. If we negate this then we have: the sky will not be dark tomorrow. Not the sky will be light tomorrow. See the difference?

Just to be nitpicky, on the apple one it is not appropriate to say most are not rotten, it could be a 50/50 split, so the "50% or more" wording is technically correct.

Good call, it's been a long day.

Micdiddy wrote:

Daily_Double wrote:

gg2 wrote:1. PT 19 S2 Q19:
there is no reason not to try my herb juice.
how is this different from "you should try my herb juice."

You're doing too much here. If I were to say that there's no reason not to exercise an option, that doesn't mean that you should exercise it. It just means there's not any reasons to not exercise it. You can't take the lack of reasons against an action to infer a reason for the action.

gg2 wrote:2. negate "most of these apples are rotten"
i got "some of the apples are not rotten"
but the answer key says: "at least half of these apples are not rotten"
how did they arrive at that answer?

Most of these apples are not rotten. Meaning that a majority are not rotten. Thus, at least half are not rotten.

gg2 wrote:3. Negate "it is unlikely that Simone will come"
i got "it is likely that Simone will come"
but the answer key says: "it is not unlikely that Simone will come".
How are they different?

It is not unlikely that Simone will come.

The summary here is that when you are negating a phrase, you simply deny the presence of the relevant action, usually by adding not. You don't take the opposite of the relevant action. For example, the sky will be dark tomorrow. If we negate this then we have: the sky will not be dark tomorrow. Not the sky will be light tomorrow. See the difference?

Just to be nitpicky, on the apple one it is not appropriate to say most are not rotten, it could be a 50/50 split, so the "50% or more" wording is technically correct.

Can you explain how it could be a 50/50 split, unless I am misunderstanding something...

I thought most always implied over 50% even if its like 50.000000001%.

So "Most of these apples are not rotten" would be over 50% of the apples are not rotten, thus negating the previous thing about "Most of the apples are rotten".

Yeah, it would be negated as: Not Most are rotten. Thus it is not the case that over 50% are rotten. Therefore at least 50% are not rotten.

Got it. thanks everyone!

Bajam wrote:

Micdiddy wrote:

Daily_Double wrote:

gg2 wrote:1. PT 19 S2 Q19:
there is no reason not to try my herb juice.
how is this different from "you should try my herb juice."

You're doing too much here. If I were to say that there's no reason not to exercise an option, that doesn't mean that you should exercise it. It just means there's not any reasons to not exercise it. You can't take the lack of reasons against an action to infer a reason for the action.

gg2 wrote:2. negate "most of these apples are rotten"
i got "some of the apples are not rotten"
but the answer key says: "at least half of these apples are not rotten"
how did they arrive at that answer?

Most of these apples are not rotten. Meaning that a majority are not rotten. Thus, at least half are not rotten.

gg2 wrote:3. Negate "it is unlikely that Simone will come"
i got "it is likely that Simone will come"
but the answer key says: "it is not unlikely that Simone will come".
How are they different?

It is not unlikely that Simone will come.

The summary here is that when you are negating a phrase, you simply deny the presence of the relevant action, usually by adding not. You don't take the opposite of the relevant action. For example, the sky will be dark tomorrow. If we negate this then we have: the sky will not be dark tomorrow. Not the sky will be light tomorrow. See the difference?

Just to be nitpicky, on the apple one it is not appropriate to say most are not rotten, it could be a 50/50 split, so the "50% or more" wording is technically correct.

Can you explain how it could be a 50/50 split, unless I am misunderstanding something...

I thought most always implied over 50% even if its like 50.000000001%.

So "Most of these apples are not rotten" would be over 50% of the apples are not rotten, thus negating the previous thing about "Most of the apples are rotten".

It really has to do with the nature of "negation." Negation isn't about providing an example that negates a statement--it is to encompass the logical opposite of a statement.

So statement: "Most are rotten."
The logical opposite is "not most are rotten." (which in turn becomes "at least 50% are not rotten")

If you say "Most are not rotten" you're going too much because a 50/50 split isn't covered by "most are not rotten."
"At least 50%" does not necessarily mean "most."

Thus, "not most are rotten" does not mean "most are not rotten"

rambleon65 wrote:
It really has to do with the nature of "negation." Negation isn't about providing an example that negates a statement--it is to encompass the logical opposite of a statement.

So statement: "Most are rotten."
The logical opposite is "not most are rotten." (which in turn becomes "at least 50% are not rotten")

If you say "Most are not rotten" you're going too much because a 50/50 split isn't covered by "most are not rotten."
"At least 50%" does not necessarily mean "most."

Thus, "not most are rotten" does not mean "most are not rotten"

Okay I can see the difference but...

How does "not most are rotten" --> "at least 50% are not rotten" ?

For some reason it doesn't come automatically to me.

gg2 wrote:

rambleon65 wrote:
It really has to do with the nature of "negation." Negation isn't about providing an example that negates a statement--it is to encompass the logical opposite of a statement.

So statement: "Most are rotten."
The logical opposite is "not most are rotten." (which in turn becomes "at least 50% are not rotten")

If you say "Most are not rotten" you're going too much because a 50/50 split isn't covered by "most are not rotten."
"At least 50%" does not necessarily mean "most."

Thus, "not most are rotten" does not mean "most are not rotten"

Okay I can see the difference but...

How does "not most are rotten" --> "at least 50% are not rotten" ?

For some reason it doesn't come automatically to me.

Just think numerically.

What does "most" mean? It means 50+1 (say out of 100). Because most means more than half, "most" cannot mean 50.
50/100 is not most.
So when you say at least 50% are not rotten, it means that most CANNOT be rotten, since for most to be rotten, 51 or more has to be rotten.

Let's do the same with 100 balls. Only two colors, yellow or blue. When you say at least 50% are yellow, it negates the statement that "most are blue." Most CANNOT be blue, because you've stated 50% are already yellow and thus more than half (definition of "most") CANNOT be blue.