"if and only if"

Comments

• akistotle Member ⭐ 🍌🍌

  January 2018 9382 karma

  This lesson talks about "if and only if":

  Advanced: Bi-Conditionals
  https://7sage.com/lesson/advanced-bi-conditionals/

  It's not "T->M or M->T" but it is "T->M and M->T"
• Don_Draper Alum Member

  January 2018 88 karma

  @akistotle said:
  This lesson talks about "if and only if":

  Advanced: Bi-Conditionals
  https://7sage.com/lesson/advanced-bi-conditionals/

  It's not "T->M or M->T" but it is "T->M and M->T"

  Thanks, I haven't gotten there in the CC.
• Trust But Verify Alum Member

  January 2018 432 karma

  The conditional lessons are crucial. You'll mentally enjoy.
• Seeking Perfection Alum Member

  January 2018 4428 karma

  @teetime64 said:
  Does this phrase introduce the sufficient or necessary condition? Ex. Tina will enter the pool, if and only if Mike enters.

  T->M
  or
  M->T

  Thanks!

  PS, I'm thinking it is the latter of the two.

  As @akistotle noted it's both.
  The if gives us
  M-->T
  If Mike enters then Tina will enter.

  The only if gives us
  T-->M
  Only if Mike enters will Tina enter. So if Tina enters Mike must have entered.

  And also as you can probably see, both
  ¬T --> ¬M
  from M-->T

  and
  ¬M -->¬T
  from T-->M

  Biconditionals are powerful things!