The twin sisters

I used to live next to a town where a pair of notorious identical twin sisters lived. Their names are Emma and Sophia. Emma always lies on Monday, Wednesday, and Friday; on other days of the week she always tells the truth. Sophia always lies on Tuesday, Friday, and Saturday; on other days of the week she always tells the truth.

The other day I met the twins, and asked one of them:

  • Who are you?
  • I am Emma.
  • What day is today?
  • Yesterday was Sunday.

The other twin added:

  • Tomorrow is going to be Friday.

I was surprised — how could it be — and asked her:

  • Are you telling the truth?

And she said:

  • I’m always telling the truth on Wednesdays.

The twins got me confused, but after a while I figured out who was who, and I even figured out what day it was.

Can you?