Sufficient and Necessary Diagramming help

[cls]

It actually makes perfect sense.

Thanks!

[cls]

Hi Nikki,

Just testing myself. If a statement reads "Only the best tomatoes are used in our pasta. Therefore, if this is not one of our pastas it cannot contain the best tomatoes."

I recognize this as a Mistaken Negation, but I wanted to double check my diagramming.

Sentence one: P T

Sentence two: P T

Am I understanding it correctly?

Thanks.

[Dave Killoran]

Hi CLS,

Yes, you are--congrats!

Fyi, I edited your diagramming to add actual negations for the ease of other readers.

Thanks!

[cls]

Hi,

I have a few more questions (want to check my progress/understanding)

Suppose a statement read:

1) "Board members cannot give a donation without going bankrupt."

Could this also be interpreted as: "if a board member donates he will go bankrupt?"

2) "James goes to church everyday, but Friday."

This is the same as "if James goes to church then it is not Friday" correct?

3) "Unless we protect human rights, they will be violated"

Same thing as "if we protect human rights, they won't be violated"? SO PHR NV


Thank you.

[Jon Denning]

Hey cls,

Thanks for the additional questions! I know these were for Dave, but I'll jump in and add my two cents

1) Yes! That would be diagrammed as:

Donate Bankrupt

So any phrasing indicating that relationship (such as, "If a board member donates he will go bankrupt") is correct.

2) Yes again! This is conditional as well:

Church Not Friday

And the contrapositive:

Friday Not Church

3) Careful! You've committed a Mistaken Reversal here. What we are told is that Protection is required for rights not to be Violated, but it does not guarantee no violation.

Let's look at the statement and its contrapositive in diagram form:

Not Violated Protect

Contrapositive:

Not Protect Violated

Essentially, the only way that rights won't be violated is if we protect them
(Not Violated Protect). Similarly, if we don't protect human rights they will be violated (Not Protect Violated).

There's a simple equation of sorts for "unless" (as well as "until," "except," and "without"):

Whatever is modified by "unless" becomes the Necessary condition, and the
remainder is negated and becomes the sufficient condition.

Let's look at the statement "Unless we protect human rights, they will be violated" with that in mind:

"unless" modifies "Protect" so it becomes necessary; Violated is the remainder so
it is negated to "Not Violated" and becomes sufficient:

Not Violated Protect

Contrapositive:

Not Protect Violated


I hope that helps! Keep practicing and you'll find these get easier and easier.

Thanks!

Jon