Page 1 of 2

What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:06 pm
by wanderlust
A-->B+C
Thanks!!

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:08 pm
by icouldbuyu
wanderlust wrote:A-->B+C
Thanks!!
not b or not c--->not a

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:08 pm
by musicfor18
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:09 pm
by Ginj
icouldbuyu wrote:
wanderlust wrote:A-->B+C
Thanks!!
not b or not c--->not a
This one.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:20 pm
by TommyK
.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:29 pm
by ScottRiqui
I think both answers given so far are equivalent, since

~(B AND C) == (~B OR ~C)

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:31 pm
by Arlington
Yep, they are logically equal.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:40 pm
by wanderlust
ScottRiqui wrote:I think both answers given so far are equivalent, since

~(B AND C) == (~B OR ~C)
but ~(B AND C) =/=~B and ~C

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:49 pm
by ScottRiqui
wanderlust wrote:
ScottRiqui wrote:I think both answers given so far are equivalent, since

~(B AND C) == (~B OR ~C)
but ~(B AND C) =/=~B and ~C

I guess it depends on how you convert musicfor18's text (If not BOTH B and C) into symbols.

I read it as ~(B AND C), rather than (~B AND ~C).

To me, the "BOTH" qualifier means that B and C go together in the parentheses with an AND, and that the NOT notation applies to the entire parenthetical statement.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 2:55 pm
by SchopenhauerFTW
Original: A --> B+C

Contrapositive: ~B or ~C --> ~A


If B is absent but C is there, then A is absent. If B is there but C is absent, then A is absent. If both B and C are absent, then A is absent. I wouldn't write ~B and ~C --> ~A because all it takes is for either B or C to be absent to have A be absent.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 3:39 pm
by robotclubmember
SchopenhauerFTW wrote:Original: A --> B+C

Contrapositive: ~B or ~C --> ~A


If B is absent but C is there, then A is absent. If B is there but C is absent, then A is absent. If both B and C are absent, then A is absent. I wouldn't write ~B and ~C --> ~A because all it takes is for either B or C to be absent to have A be absent.
Ignore everything else you've seen up to now and just focus on this, as it is actually correct. Only half of the other people's replies won't fuck you over on test day, lol.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 3:53 pm
by thegarciab0y
SchopenhauerFTW wrote:Original: A --> B+C

Contrapositive: ~B or ~C --> ~A


If B is absent but C is there, then A is absent. If B is there but C is absent, then A is absent. If both B and C are absent, then A is absent. I wouldn't write ~B and ~C --> ~A because all it takes is for either B or C to be absent to have A be absent.
I'm glad somebody got it correct. LGB and/or conditional statements, look it up.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 3:58 pm
by icouldbuyu
musicfor18 wrote:
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

No offense, but how did you get a 167?

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 3:59 pm
by homestyle28
DeMorgan's Law FTW!

~(A&B) ::~A v ~B
~(AvB) ::~A & ~B

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 4:02 pm
by NYC_7911
icouldbuyu wrote:
musicfor18 wrote:
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

No offense, but how did you get a 167?
Huh? As noted above, he (or she) isn't wrong. It's just worded differently. Not B or not C is the same as "not both."

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 4:07 pm
by tsutsik
icouldbuyu wrote:
musicfor18 wrote:
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

No offense, but how did you get a 167?
As was already pointed out, the answer isn't wrong. The natural way to read 'If not BOTH B and C, not A' is with the negation having wide scope in the antecedent: ~(B & C) --> ~A.

That's the right answer.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 5:29 pm
by robotclubmember
tsutsik wrote:
icouldbuyu wrote:
musicfor18 wrote:
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

No offense, but how did you get a 167?
As was already pointed out, the answer isn't wrong. The natural way to read 'If not BOTH B and C, not A' is with the negation having wide scope in the antecedent: ~(B & C) --> ~A.

That's the right answer.
Agreed, but it's still a very trippy way to say it. Most books won't say it this way, because even if people at the 90th percentile will understand it, it's a mindfuck for people under the 90th percentile.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 8:33 pm
by JazzOne
icouldbuyu wrote:
musicfor18 wrote:
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

No offense, but how did you get a 167?
No offense, but how can you be so oblivious?

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 8:45 pm
by musicfor18
My answer, although completely correct, is probably not as well worded as the other. Basically, though, if either B or C is absent, A is absent.

Re: What is the contrapositive of this statement

Posted: Wed Dec 01, 2010 8:59 pm
by moopness
JazzOne wrote:
icouldbuyu wrote:
musicfor18 wrote:
wanderlust wrote:A-->B+C
Thanks!!
Contrapositive:

If not BOTH B and C, not A.

No offense, but how did you get a 167?
No offense, but how can you be so oblivious?

Re: What is the contrapositive of this statement

Posted: Thu Dec 02, 2010 1:30 am
by benito
I love it when someone says something as condescending as "how did you get a 167" based on information they are mistaken on themselves......there was nothing wrong at all with person's explanation at all, clearly earned their 167

Re: What is the contrapositive of this statement

Posted: Thu Dec 02, 2010 2:12 am
by pressplay
Wow. The first reply was adequate. The rest was pure entertainment. :)

Re: What is the contrapositive of this statement

Posted: Thu Dec 02, 2010 2:17 am
by dakatz
Truly amazing that an incredibly simple question which was fully answered in the 1st response needs 22 responses and unnecessary namecalling.

Re: What is the contrapositive of this statement

Posted: Thu Dec 02, 2010 2:22 am
by Brock2010
dakatz wrote:Truly amazing that an incredibly simple question which was fully answered in the 1st response needs 22 responses and unnecessary namecalling.
+ One hundred thousand trillion

Re: What is the contrapositive of this statement

Posted: Thu Dec 02, 2010 2:28 am
by D. H2Oman
If not B and C ----> A