Logical Negation

Comments

• apublicdisplay Alum Member

  March 2017 edited March 2017 696 karma

  I think you're getting confused because of the many instances of "not." Just break things into the sufficient and necessary condition without focusing on the nots.

  So we have (Any candidate whose visual image does not evoke many positive feelings in votes) --> (Not be elected). Or, just X --> Y. How do you negate X --> Y? X and Not Y. So, leave the sufficient condition as is and add the negation to the necessary condition: Not (Not be elected) comes out to (being elected).

  So the negation of your statement would be: Any candidate whose visual image does not evoke many positive feelings in votes will be elected.
• Q.E.D Alum Member

  March 2017 556 karma

  You have to change the "any" to "some" as well.

  The original:
  (All candidates)(~X->~Y)

  Or "All candidates are such that if they're not pretty then they won't get elected."

  Negated:
  ~(All candidates)(~X->~Y)

  Drop the negation on the quantifier through to the sentence and change the quantifier:
  (Some candidate)~(~X->~Y)

  Or just
  (Some candidate)(~X&Y)

  Just remember "not all A are B" is the same as "some A are not B." Or, as I like to say, "not all" means "some not."

  Good luck on the test mang.