Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

No-data

  • one year ago

Why \[\forall x \in \emptyset: P(x)\] is equivalent to \[x\in \emptyset \Rightarrow P(x)\]?

  • This Question is Closed
  1. binarymimic
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    it's just how mathematicians/logicians write things down. it's a matter of notation, and nothing more. they both state the same thing in a different way. they both claim that for any x in the empty set, P(x) is true another trivial example, what if we said: E = the set of all even numbers P(x) = "x + 2 is in E" and we made this claim: For all even numbers e in E, e + 2 is in E. \[\forall e \in E, P(e)\] see how this is an equivalent statement to: "if e is in E, then e + 2 is in E" \[(e \in E) \rightarrow P(e)\]

  2. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\begin{array}{|c|c|c|}\hline\phi&\psi&\phi\Rightarrow\psi\\\hline T&T&T\\T&F&F\\F&T&T\\F&F&T\\\hline\end{array}\]\[\begin{array}{|c|c|c|c|}\hline \forall x \in \emptyset:P(x)&x\in\emptyset &P(x)& x\in\emptyset \Rightarrow P(x)\\\hline T&T&T&T\\\hline\end{array}\]

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.