Certain facts. Provable and otherwise about cookies.

  1. Mac states it is necessary, but sufficient, that his cookie be Big.

  2. For Scarlett, it is necessary and sufficient that she have a cookie.

  3. For Mac, it is sufficient—but not necessary—that Mac and Scarlett each have a cookie(cf.1).

  4. For Scarlett, it is sufficient—but not necessary—that Scarlett and Mac each have a cookie(cf.1).

  5. Statements #3 and #4 are not identical. The proof is left for the reader.