What is the contrapositive of this statement

Prepare for the LSAT or discuss it with others in this forum.
wanderlust

Posts: 66
Joined: Sat Nov 06, 2010 12:02 pm

What is the contrapositive of this statement

A-->B+C
Thanks!!

Posts: 254
Joined: Sun Oct 24, 2010 3:52 pm

Re: What is the contrapositive of this statement

wanderlust wrote:A-->B+C
Thanks!!

not b or not c--->not a

musicfor18

Posts: 692
Joined: Mon Feb 09, 2009 9:15 pm

Re: What is the contrapositive of this statement

wanderlust wrote:A-->B+C
Thanks!!

Contrapositive:

If not BOTH B and C, not A.

Ginj

Posts: 530
Joined: Tue Aug 31, 2010 11:53 am

Re: What is the contrapositive of this statement

wanderlust wrote:A-->B+C
Thanks!!

not b or not c--->not a

This one.

TommyK

Posts: 1309
Joined: Fri Jun 25, 2010 3:08 pm

Re: What is the contrapositive of this statement

.
Last edited by TommyK on Wed Dec 01, 2010 4:00 pm, edited 1 time in total.

ScottRiqui

Posts: 3637
Joined: Mon Nov 29, 2010 8:09 pm

Re: What is the contrapositive of this statement

I think both answers given so far are equivalent, since

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

Arlington

Posts: 3
Joined: Sat Dec 05, 2009 8:45 pm

Re: What is the contrapositive of this statement

Yep, they are logically equal.

wanderlust

Posts: 66
Joined: Sat Nov 06, 2010 12:02 pm

Re: What is the contrapositive of this statement

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

ScottRiqui

Posts: 3637
Joined: Mon Nov 29, 2010 8:09 pm

Re: What is the contrapositive of this statement

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.

SchopenhauerFTW

Posts: 1793
Joined: Sun Oct 10, 2010 10:22 pm

Re: What is the contrapositive of this statement

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.

robotclubmember

Posts: 743
Joined: Wed Sep 15, 2010 7:53 am

Re: What is the contrapositive of this statement

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.

thegarciab0y

Posts: 60
Joined: Sat Nov 13, 2010 6:32 pm

Re: What is the contrapositive of this statement

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.

Posts: 254
Joined: Sun Oct 24, 2010 3:52 pm

Re: What is the contrapositive of this statement

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?

homestyle28

Posts: 2362
Joined: Thu Jun 04, 2009 12:48 pm

Re: What is the contrapositive of this statement

DeMorgan's Law FTW!

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

NYC_7911

Posts: 238
Joined: Sat Oct 30, 2010 9:03 pm

Re: What is the contrapositive of this statement

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."

tsutsik

Posts: 111
Joined: Wed Aug 12, 2009 5:26 pm

Re: What is the contrapositive of this statement

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.

robotclubmember

Posts: 743
Joined: Wed Sep 15, 2010 7:53 am

Re: What is the contrapositive of this statement

tsutsik 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.

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.

JazzOne

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

Re: What is the contrapositive of this statement

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?

musicfor18

Posts: 692
Joined: Mon Feb 09, 2009 9:15 pm

Re: What is the contrapositive of this statement

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.

moopness

Posts: 310
Joined: Fri Jul 16, 2010 8:56 pm

Re: What is the contrapositive of this statement

JazzOne 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?

benito

Posts: 321
Joined: Wed Oct 27, 2010 10:09 pm

Re: What is the contrapositive of this statement

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

pressplay

Posts: 5
Joined: Fri Nov 26, 2010 6:06 am

Re: What is the contrapositive of this statement

dakatz

Posts: 2422
Joined: Sat Mar 29, 2008 4:19 pm

Re: What is the contrapositive of this statement

Truly amazing that an incredibly simple question which was fully answered in the 1st response needs 22 responses and unnecessary namecalling.

Brock2010

Posts: 82
Joined: Thu Dec 02, 2010 1:01 am

Re: What is the contrapositive of this statement

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

D. H2Oman

Posts: 7446
Joined: Tue Feb 24, 2009 5:47 am

Re: What is the contrapositive of this statement

If not B and C ----> A