Negating the conditional statement (for NA question)

Comments

• 1 Like

  Wombat15 Member

  January 2015 67 karma

  "If you get an 180 on the LSAT, your chances of getting into T3 do NOT increase".
• alex.yousif9 Free Trial Member

  January 2015 edited January 2015 3 karma

  "If you get 180 on LSAT, [then] your chances of getting into T3 increase" is a material conditional of the form P-->Q. These conditionals are logically equivalent to (~P v Q) (that is, ‘not P or Q') by the material implication rule. The negation is ~(~P v Q), and this is equivalent to P & ~Q (by an application of De Morgan’s rule and double negation). So the negation of the statement that "If you get 180 on LSAT, your chances of getting into T3 increase", is that “you get 180 on the LSAT, AND it is not the case that your chances of getting into T3 increases.”
  
  Wombat maintains that the negation of your conditional would be the following:
  "If you get an 180 on the LSAT, your chances of getting into T3 do NOT increase".
  
  This is symbolized as follows: (P --> ~Q); but by the implication rule we get ~P v ~Q. But by DeMorgan and Double Negation, we get the logically equivalent statement P & Q. And P&Q is obviously not logically equivalent to the (P & ~Q), which we showed was the negation of (P—>Q). So Wombat is mistaken.