Mac states it is necessary, but sufficient, that his cookie be Big.
For Scarlett, it is necessary and sufficient that she have a cookie.
For Mac, it is sufficient—but not necessary—that Mac and Scarlett each have a cookie(cf.1).
For Scarlett, it is sufficient—but not necessary—that Scarlett and Mac each have a cookie(cf.1).
Statements #3 and #4 are not identical. The proof is left for the reader.