contrapositive LG

senorhosh
Posts: 470
Joined: Tue Dec 28, 2010 4:45 am

contrapositive LG

Postby senorhosh » Wed Jun 22, 2011 7:57 pm

For grouping games:
Is it safe to assume that 100% of the time, a contrapositive can be made by reversing the arrows and slash marks?

For example:
A --> B (If A is chosen B is chosen)
Contrapositive:
B --> A (If B is not chosen, A is not chosen)

Or example #2
A --> B (if A is not chosen, B is chosen)
Contrapositive:
B --> A (If B is not chosen, A is chosen)

Seems like it's been working everytime. Before I start relying on this, are there instances when this is NOT true??

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Verity
Posts: 1253
Joined: Sun Jan 30, 2011 11:26 pm

Re: contrapositive LG

Postby Verity » Wed Jun 22, 2011 8:00 pm

It's always true. It's a logical rule, it's not contingent on the game type.

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Campagnolo
Posts: 906
Joined: Wed Oct 28, 2009 5:49 pm

Re: contrapositive LG

Postby Campagnolo » Wed Jun 22, 2011 8:00 pm

The contrapositive is always equivalent to the original statement, whether in the games section, the logical reasoning section, or any other time whatever.

Rely on it.

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EarlCat
Posts: 610
Joined: Mon Mar 12, 2007 4:04 pm

Re: contrapositive LG

Postby EarlCat » Wed Jun 22, 2011 8:55 pm

Flip, negate, swap "and" and "or."

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cogitoergosum
Posts: 788
Joined: Tue May 31, 2011 7:13 pm

Re: contrapositive LG

Postby cogitoergosum » Wed Jun 22, 2011 10:27 pm

I find it helpful to think of it this way:

Example 1:
A-->B: if A occurs, then B must occur

Contrapositive:
NOT B --> NOT A: If B does not occur, then it is not possible that A occurred (because if A had occurred, then we know from the original conditional statement above that B would have occurred)

Example 2:
A and B --> C: if both A and B occur, then C must occur

Contrapositive:
NOT C --> NOT A or NOT B (either A or B [or both] must not have occurred, because if both had occurred, then we know from the original conditional statement above that C would have occurred)

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joebloe
Posts: 376
Joined: Mon Nov 08, 2010 6:02 am

Re: contrapositive LG

Postby joebloe » Thu Jun 23, 2011 11:02 am

Campagnolo wrote:The contrapositive is always equivalent to the original statement, whether in the games section, the logical reasoning section, or any other time whatever.

Rely on it.


This. By the time you hit test day, you should be able to form a contrapositive in your sleep, and should be doing it automatically whenever a question seems to contain logical implications.




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