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If but only if

General questions relating to the LSAT Logic Games.
 ellenb
  • Posts: 260
  • Joined: Oct 22, 2012
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-  Fri Nov 16, 2012 11:41 pm #6509
Dear Powerscore,

I was just curious on how to diagram a "if but only if" statement. I know how to diagram "if and only if" but I was confused how to diagram when it has a but. Also, what would be the contrapositive for a "if but only if" statement.


Thanks

Ellen
User avatar
 Dave Killoran
PowerScore Staff
  • PowerScore Staff
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  • Joined: Mar 25, 2011
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-  Sat Nov 17, 2012 10:20 am #6513
Hi Ellen,

"If and only if" is identical to "if but only if," and both are diagrammed as: A :dbl: B

The individual components of those double arrows are:

..... ..... ..... A if B: ..... ..... B :arrow: A
..... ..... and/but
..... ..... ..... A only if B: ..... A :arrow: B

The contrapositive of each individual statement is:

..... ..... ..... A :arrow: B

..... ..... ..... B :arrow: A


When we add those two together, they form the contrapositive of the double-arrow:

..... ..... ..... A :dbl: B

(that's not-A and not-B in case the strikethroughs aren't clear)

Please let me know if that helps. Thanks!
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