0

So I'm trying to prove the validity of this formula and I am a bit lost, not sure how to start. I know generally speaking a valid formula is one where if all the premises are true, then the conclusion can not be false, but I don't know how to prove this really. any help is appreciated

http://imgur.com/jop9Gq3

Bardia
  • 13
  • 2
  • 5
    See the comments on [this](http://math.stackexchange.com/questions/1144141/is-the-formula-logically-valid) question. – Git Gud Jun 28 '16 at 21:55

1 Answers1

0

Convert to the contrapositive:$$\exists y((\exists x.S(x))\implies S(y))$$with $S=\lnot R$, and maybe it's a little easier to analyse. Simply put, if $\exists x.S(x)$, then there exists a $y$ such that the conclusion, $S(y)$ is true, and the formula is valid. If there is no such $x$, then the formula is vacuously true.

Arthur
  • 193,927
  • 14
  • 168
  • 299