Why do we Bentch?

ואכלת ושבעת וברכת    

Why do we Bentch?

Is it to thank Hashem for the pleasure of:

1) eating

2) full stomach

3) both eating & full

 

R.Akivah Eiger ( 'הגהות רע"א או"ח רפ"ו: ב ) asks a

חקירה:

 What creates  the חיוב  of Bentching, is it both the אכילה & שביעה (eating & being full) or maybe only the שביעה creates  the חיוב and not the אכילה

It would make a difference if,



1) A קטן who became A גדול within 72 minutes (כדי עיכול)
(time it takes for food to digest) of eating a meal that he
has Bentched as a קטן. Is he obligated to Bentch again?
The אכילה  was done as a קטן and the שביעה as a גדול
(R. A. Eiger )

2) A Goy who ate and became a גר
within 72 minutes of his meal, Is he obligated
to Bentch for eating when he was a Goy?


3) According to the שיטות that women are פטור
from Birkat Hamazon An עבד כנעני (same as women)
who ate and his master freed him within 72 minutes
of his meal is he obligated to Bentch?

4) An אונן who ate and they buried the Niftar
within 72 minutes of his meal, Is he obligated
to Bentch?
(Chochmas Adam)

5) A קטן ate before his Bar Mitzvah and wasn't full
he became Bar Mitzvah within 72 minutes and
ate a small amount (פחות מכשיעור שביעה) which filled
him up. Is he obligated to Bentch again even though
he ate less than a Shiur since he is full.?
(Harav Zvi Pesach Frank ZT"l)