Formal Logic Help Forum

[SecondWind]

Can a couple people please confirm that I have converted/conjugated/translated this correctly or offer advice on how to correct it?

Original: I never wear my dress without wearing my hat. = ~H →~D
Original simplified: I do not wear my dress if I am not wearing my hat. = ~H →~D
Positive: I wear my dress if am I wearing my hat. = H →D
Contra: If I'm not wearing my hat then I'm not wearing my dress. = ~D→ ~H

The Necessary phrase in the Original = "I never wear my dress"
The Sufficient phrase in the Original = "without wearing my hat"

The Necessary phrase in the Contra = "then I'm not wearing my dress"
The Sufficient phrase in the Contra = "If I'm not wearing my hat"

Also, she can wear her hat and not wear her dress and still be within the "rules" correct?

Thanks in advance!

KCCO

-Cody

[Daily_Double]

Can a couple people please confirm that I have converted/conjugated/translated this correctly or offer advice on how to correct it?

Original: I never wear my dress without wearing my hat. = ~H →~D
Original simplified: I do not wear my dress if I am not wearing my hat. = ~H →~D
Positive: I wear my dress if am I wearing my hat. = H →D
Contra: If I'm not wearing my hat then I'm not wearing my dress. = ~D→ ~H

The Necessary phrase in the Original = "I never wear my dress"
The Sufficient phrase in the Original = "without wearing my hat"

The Necessary phrase in the Contra = "then I'm not wearing my dress"
The Sufficient phrase in the Contra = "If I'm not wearing my hat"

Also, she can wear her hat and not wear her dress and still be within the "rules" correct?

Thanks in advance!

KCCO

-Cody

You made a mistaken negation in the first line of the bolded phrases, and you mis-diagrammed the second line. To answer your question in the line italicized, yes. She can wear the hat without the dress, but she cannot wear the dress without the hat. Here's is all we know:

Original: (there's a couple ways to interpret this)

Powerscore's way: Uses the unless equation, which is where the phrase referred to by unless, until, without, except is the necessary condition and the other condition is first negated, and then made the sufficient condition:

dress ---> Hat
If this person is wearing a dress, then she is wearing a hat. (I'm picturing a sundress at the Kentucky Derby)

The other way: More common sense, negates the phrase referred to by unless, until, without, except, and makes it the sufficient condition, while the other is not negated and becomes the necessary condition

~(Hat) ---> ~(Dress)
If she's not wearing a hat, then she's not wearing a dress

Contrapositive: depends upon which method you used above, if you choose Powerscore's method, then the contrapositive is the other one, and if you choose the other one then the contrapositive is Powerscore's classification. The above two things are all we know.

[SecondWind]

The other way: More common sense, negates the phrase referred to by unless, until, without, except, and makes it the sufficient condition, while the other is not negated and becomes the necessary condition.

Thanks for a swift reply.

In the bolded statement, is the phrase that you are referring to which becomes the sufficient condition "If she's not wearing a hat" ?

[Daily_Double]

The other way: More common sense, negates the phrase referred to by unless, until, without, except, and makes it the sufficient condition, while the other is not negated and becomes the necessary condition.

Thanks for a swift reply.

In the bolded statement, is the phrase that you are referring to which becomes the sufficient condition "If she's not wearing a hat" ?

Yeah, using that approach the phrase which is negated and becomes the sufficient condition is without a hat. I say negated because using Powerscore's approach it becomes the necessary condition and goes "If x ---> wearing hat. But in this case it becomes "If not hat ---> not x"

[SecondWind]

The other way: More common sense, negates the phrase referred to by unless, until, without, except, and makes it the sufficient condition, while the other is not negated and becomes the necessary condition.

Thanks for a swift reply.

In the bolded statement, is the phrase that you are referring to which becomes the sufficient condition "If she's not wearing a hat" ?

Yeah, using that approach the phrase which is negated and becomes the sufficient condition is without a hat. I say negated because using Powerscore's approach it becomes the necessary condition and goes "If x ---> wearing hat. But in this case it becomes "If not hat ---> not x"

Thanks for your help. Stickers and brownie points for you!

[nyjets2090]

With until, unless, except, without, I would cross it out in the question and write "if not" just to make it easy on myself.

[bp shinners]

With until, unless, except, without, I would cross it out in the question and write "if not" just to make it easy on myself.

Yep, that's what I do.