Need help with TOUGH conditional statement Forum

[youknowryan]

How do I symbolize:

No tax reduction package that would greatly inconvenience parents will be adopted this year.

Is it:

Rule: Tax Reduction Package Adopted - > ~Greatly Inconvenience Parents

Contra: Greatly Inconvenience Parents - > ~Tax Reduction Package Adopted

OR

Rule: ~Greatly Inconvenience Parents - > Tax Reduction Package Adopted

Contra: ~Tax Reduction Package Adopted - > Greatly Inconvenience Parents

I think it is the former, but any clarification would be appreciated. Please explain your rationale.

[KaplanLSATInstructor]

The former is more accurate. Consider what the sentence is saying in other words:

This year, we're not going to adopt any package that would greatly inconvenience parents. So, if it greatly inconveniences parents, it will not be adopted this year:

inconv --> no adopt
adopt --> won't inconv.

Sometimes, rewording the sentence helps clarify the logic. And remember: No X are Y translates to X --> Not Y. (For example, "No dogs have wings" translates to "dog --> no wings")

HTH

- Chris

[youknowryan]

inconv --> no adopt
adopt --> won't inconv.

I see that you changed the order from what I had: is the top one the rule and the bottom the contrapositive?

[KaplanLSATInstructor]

It doesn't matter -- both statements say the exact same thing, just in different ways. My original rule is just the contrapositive of your original rule and your original rule is just the contrapositive of mine.

There's no definitive "original" and "contrapositive." A contrapositive is merely a way of writing a logically equivalent version of whatever you wrote in the first place. As long as what you write is accurate, the logic will be exactly the same in both statements.

[dakatz]

There is no "original". Each conditional statement can be written two ways. "Contrapositive" simply means that you are negating the necessary condition of whichever way you chose to write the statement REGARDLESS of which one you decide to write first. I believe they say this in a Powerscore book, but would you look at a penny and think one side is more valuable than the other? They are the exact same thing written in two different ways.

[quasi-stellar]

No tax reduction package that would greatly inconvenience parents will be adopted this year.

The way i see it (not necessarily correct) is like this:
Greatly inconveniencing parents -> package will not be adopted.

The question of convenience seems sufficient to determine the course of action.
so if adopted, the package is not inconvenient to the parents, which is basically cp of what i wrote above.

Feel free to comment if my reasoning is flawed On a side note, I am not even sure this is a conditional statement in the first place. But its ok.

[TheLuckyOne]

How do I symbolize:

No tax reduction package that would greatly inconvenience parents will be adopted this year.

Is it:

Rule: Tax Reduction Package Adopted - > ~Greatly Inconvenience Parents

Contra: Greatly Inconvenience Parents - > ~Tax Reduction Package Adopted

OR

Rule: ~Greatly Inconvenience Parents - > Tax Reduction Package Adopted

Contra: ~Tax Reduction Package Adopted - > Greatly Inconvenience Parents

I think it is the former, but any clarification would be appreciated. Please explain your rationale.

An easy way to do it is to rephrase a sentence by moving negation into the other clause:

Any tax reduction package that would greatly inconvenience parents will not be adopted this year. In other words, if inconvenient, then won't be adopted.

Inconvenient --> -Adopted

[youknowryan]

It doesn't matter -- both statements say the exact same thing, just in different ways. My original rule is just the contrapositive of your original rule and your original rule is just the contrapositive of mine.

There's no definitive "original" and "contrapositive." A contrapositive is merely a way of writing a logically equivalent version of whatever you wrote in the first place. As long as what you write is accurate, the logic will be exactly the same in both statements.

I'm with you here: I've been reading the LGB and am obsessed with the rule/contrapositive model they proffer. Thanks for the input.

[TrojanHopeful]

For a statement that starts with "No": The part that immediately follows "no" is the sufficient condition; if you negate the rest of the statement then you get the necessary condition.

Sufficient = tax reduction package that would greatly inconvenience parents

Necessary = will not be adopted this year.

inconvenience parents > will not be adopted

will be adopted > does not inconvenience parents

[quasi-stellar]

For a statement that starts with "No": The part that immediately follows "no" is the sufficient condition; if you negate the rest of the statement then you get the necessary condition.

Sufficient = tax reduction package that would greatly inconvenience parents

Necessary = will not be adopted this year.

inconvenience parents > will not be adopted

will be adopted > does not inconvenience parents

Worrrrd. This pretty much sums it up