How to negate this statement?

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ioannisk

Posts: 83
Joined: Wed Jul 31, 2013 11:38 am

How to negate this statement?

How to negate this statement?

"If Murray did not have a felony convinction, he would be accepted for the position of Executive Adminstrator"

With statements like these, do you put the "not" into the sufficient or the necessary condition? Why?

How does ""If Murray did not have a felony convinction, he would be accepted for the position of Executive Adminstrator" differ from ""If every person did not have a felony convinction, every person would be accepted for the position of Executive Adminstrator"?

For example, if you were to negate it, would you change it to ""If every person did not have a felony convinction, some persons would be accepted for the position of Executive Adminstrator"?

Or

""If some persons did not have a felony convinction, every person would be accepted for the position of Executive Adminstrator"?

Why? If i'm correct for either negation, why would I use the logical opposite "some" over using "not" to negate it?

JazzOne

Posts: 2980
Joined: Tue Sep 09, 2008 11:04 am

Re: How to negate this statement?

ioannisk wrote:How to negate this statement?

"If Murray did not have a felony convinction, he would be accepted for the position of Executive Adminstrator"

With statements like these, do you put the "not" into the sufficient or the necessary condition? Why?

How does ""If Murray did not have a felony convinction, he would be accepted for the position of Executive Adminstrator" differ from ""If every person did not have a felony convinction, every person would be accepted for the position of Executive Adminstrator"?

For example, if you were to negate it, would you change it to ""If every person did not have a felony convinction, some persons would be accepted for the position of Executive Adminstrator"?

Or

""If some persons did not have a felony convinction, every person would be accepted for the position of Executive Adminstrator"?

Why? If i'm correct for either negation, why would I use the logical opposite "some" over using "not" to negate it?

Conditional statements are difficult to negate. Let's consider your first example:

No felony convictions for Murrary -> Murray accepted for position

Essentially, every conditional statement describes a relationship between two ideas. One is necessary, and one is sufficient. The negation of every conditional is simply that the necessary/sufficient relationship does NOT exist. To reference our example above, the negation would be: "Murray's lack of felony convictions does NOT necessarily guarantee that he will be accepted to the position.
Last edited by JazzOne on Tue Oct 22, 2013 3:21 pm, edited 1 time in total.

JazzOne

Posts: 2980
Joined: Tue Sep 09, 2008 11:04 am

Re: How to negate this statement?

ioannisk wrote:How to negate this statement?

"If Murray did not have a felony convinction, he would be accepted for the position of Executive Adminstrator"

With statements like these, do you put the "not" into the sufficient or the necessary condition? Why?

How does ""If Murray did not have a felony convinction, he would be accepted for the position of Executive Adminstrator" differ from ""If every person did not have a felony convinction, every person would be accepted for the position of Executive Adminstrator"?

For example, if you were to negate it, would you change it to ""If every person did not have a felony convinction, some persons would be accepted for the position of Executive Adminstrator"?

Or

""If some persons did not have a felony convinction, every person would be accepted for the position of Executive Adminstrator"?

Why? If i'm correct for either negation, why would I use the logical opposite "some" over using "not" to negate it?

Here's your second example, for clarification.

Every person has no felony convictions -> every person accepted to position

The negation could be stated: "If nobody has a felony conviction, that would NOT guarantee that every person is accepted to the position."
Last edited by JazzOne on Tue Oct 22, 2013 3:25 pm, edited 3 times in total.

PourMeTea

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Joined: Sun Jun 17, 2012 8:32 am

Post removed.

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Last edited by PourMeTea on Fri May 08, 2015 12:19 am, edited 1 time in total.

ioannisk

Posts: 83
Joined: Wed Jul 31, 2013 11:38 am

Re: How to negate this statement?

thanks guys, makes perfect sense

iamgeorgebush

Posts: 908
Joined: Sat Oct 05, 2013 3:57 pm

Re: How to negate this statement?

OP:

If you're looking to a way to negate it in the way that one negates an AC for a necessary assumption question and the statement "If Murray did not have a felony convinction, he would be accepted for the position of Executive Administrator" is the AC, then you might say "Murray did not have a felony conviction, and he was not be accepted for the position of Executive Administrator."

bp shinners

Posts: 3086
Joined: Wed Mar 16, 2011 7:05 pm

Re: How to negate this statement?

Negating a conditional statement is essentially crossing out the arrow - the sufficient condition is no longer sufficient; the necessary condition is no longer necessary.

My go to example:
All blondes are dumb.
B-->D
But Julia Stiles went to Columbia, and Dolph Lundgren is an astrophysicist in his spare time (seriously). So my original condition must be wrong; i.e. I should negate it.

Would that be B-->Not D? Nope - Paris Hilton exists.

Instead, it would be, "Being blonde doesn't guarantee that you're dumb" or "A blonde person isn't necessarily dumb". Or any similar phrase.