Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difference between only if and if and only if

  1. Jan 8, 2014 #1
    Difference between "only if" and "if and only if"

    $$1.\quad p\quad if\quad q\\ \equiv if\quad q\quad then\quad p\\ \equiv q\rightarrow p\\ \\$$$$2.\quad p\quad only\quad if\quad q\\ \equiv if\quad p\quad then\quad q\\ \equiv p\rightarrow q\\ \\$$$$3.\quad p\quad only\quad if\quad q\\ \equiv if\quad q\quad then\quad p\\ \equiv q\rightarrow p\\ \\$$$$4.\quad p\quad iff\quad q\\ \equiv (p\rightarrow q)\wedge (q\rightarrow p)$$

    I think #3 is wrong but I'm not sure why.
     
    Last edited: Jan 8, 2014
  2. jcsd
  3. Jan 8, 2014 #2
    Yes, #3 is wrong. The second line says if q, then p, but we know that p may only occur when q does from the first line.

    If q, then p allows p to occur without q.
     
  4. Jan 8, 2014 #3

    jedishrfu

    Staff: Mentor

  5. Jan 15, 2014 #4

    ssd

    User Avatar

    p only if q
    ⇔ q if p.
    So the first line in (3) does not imply the second line.
     
  6. Jan 31, 2014 #5

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    I watch the "Teletubbies" show only if I have a TV. I have a TV, but I would rather tear out my eyes than watch Teletubbies. So p only if q is not the same as q implies p.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Difference between only if and if and only if
  1. If and only if (Replies: 8)

Loading...