How do you negate this sentence to logical opposite? Forum

[aena]

"Unless the stock market rebounds, the economy will not recover this year."
How does this sentence negate to:

"The economy will recover this year even if the stock market rebound."

Could someone tell me how to rearrange the unless sentence to If/then form?
I thought, for conditional statements, logical opposites occur as:

A -----> B
A -----> NOT B

This is so confusing
THANKS.

[oaken]

The negation of the first sentence is "if the economy recovers this year, then the stock market rebounded."

[Br3v]

With "unless", this is what you do.

After "unless" introduces the necessary part.
The remaining left over part is the sufficient condition, but you must negate it first.

Example:
A unless B

Take the part after unless for necessary
>B
Now negate the other remaining conditional for the sufficient
NOT A > B

Example 2:
Unless you are dead, you are breathing.

Take the part after unless
> you are dead
Take the remaining and negate it
If you are NOT breathing> then you are dead

[CardozoLaw09]

Unless (necessary condition), (sufficient condition).
When unless is placed in front of the statement, it reverses the "if, then" ie) the necessary comes first and the sufficient is what follows when normally if it was in "if, then" format the sufficient would come after the 'if' and the necessary after the 'then.'

Sufficient condition --> necessary condition

So, IF the economy will recover this year (P), then the stock market has rebounded (Q).

If P --> Q
Contrapositive:
~Q --> ~P

[Br3v]

With "unless", this is what you do.

After "unless" introduces the necessary part.
The remaining left over part is the sufficient condition, but you must negate it first.

Example:
A unless B

Take the part after unless for necessary
>B
Now neate the other remaining conditional for the sufficient
NOT A > B

Example 2:
Unless you are dead, you are breathing.

Take the part after unless
> you are dead
Take the remaining and negate it
If you are NOT breathing> then you are dead

Dammit I gave you advice for contra positive, didn't see you were asking for just the logical opposite

[aena]

Thank you, br3v and cardozo...

Actually, I think the negation is:
"The economy will recover this year even if the stock market DOES NOT rebound."

I realized it's just written in contra positive form. B -----> Not A

But thank you for your lessons on sufficient/necessary on unless!! very helpful!

[aena]

Nevermind, I still don't get this
Like they said,

A = the economy will not recover,
B = unless stock market rebounds,

Original: A ----> B
Negation : A ----> not B

But BOTH A and B are negated in the correct answer which is "even if stock market does notrebound, the economy will recover.

...help.

[oaken]

Nevermind, I still don't get this
Like they said,

A = the economy will not recover,
B = unless stock market rebounds,

Original: A ----> B
Negation : A ----> not B

But BOTH A and B are negated in the correct answer which is "even if stock market does notrebound, the economy will recover.

...help.

Maybe I'm not understanding what you're asking, but the original sentence is essentially saying "It is required that the stock market rebounds for the economy to recover." Therefore, a logical opposite could be "It is NOT required that the stock market rebound for the economy to recover," or maybe "The economy can recover even without the stock market rebounding." Does that help?

[anon sequitur]

Yeah, this is a confusing idea that is not handled well in the LRB. Long story short, the negation of a conditional is NOT another conditional statement. Oaken's two proposed negations in the message above are correct; note that they are not conditional statements. "Even if" isn't conditional.

Try thinking about very simple conditional statements:

All kittens are cute = K --> C

The negation of this is should not be thought of as K --> ~C

That would be incorrect because to negate the idea that all kittens are cute, you need only show that some kittens are not cute, not necessarily that none of them are cute. Think of it like this: K --> C implies that 100% of kittens are cute. The negation of that is just "not 100%", which could be anything from 0-99.9%. So you just want to say "some kittens are not cute" or "not all kittens are cute".

For unless statements it works the same way, just paraphrase them into if/then statements first to have an easier time of it.

Unless the stock market rebounds, the economy will not recover this year.
translates to: If the economy recovers, the stock market rebounds. So:

ER --> MR

The negation of that is, ER, yet not MR. The economy may recover even if market doesn't rebound.

Keep in mind the difference between logical and polar opposites. The polar opposite is rarely important or useful on the LSAT, but it's important to recognize how it's different from the logical opposite.

A --> B
polar opposite = A --> ~B
logical opposite = A & ~B

[bp shinners]

ER --> MR

The negation of that is, ER, yet not MR. The economy may recover even if market doesn't rebound.

Perfect way of stating it. When you negate a conditional, you essentially cross out the arrow. The sufficient no longer guarantees the necessary (i.e. you can have the sufficient condition without the necessary condition).