Premise:
"that's over a year ago and it's it hasn't had any problems yeah seemed to"
Hypothesis: It hasn't had any problems for over a year

yes

Premise:
"Ware's group has developed the mental-health segment first."
Hypothesis: Ware's group was the first to develop the mental-health segment.

yes

Premise:
"He held an open letter in his hand."
Hypothesis: He has a letter that is open.
yes