Gmat Manhattan Sentence Correction Guide, Chapter 13, Pg 263, (Problem Set) question 3.
The original Sentence: "When he swam across the lake, he struggled to keep his head above water."
I understand the above sentence is correct. I want to understand whether following three constructions of the above sentence are grammatically correct and convey the same meaning?
a) When he swam across the lake, he was struggling to keep his head above water.
b) When he was swimming across the lake, he struggled to keep his head above water.
c) When he was swimming across the lake, he was struggling to keep his head above water.
My hypothesis is that they are grammatically correct and convey the same meaning. Please validate.