Past Paper - State Spaces

Hey all,

Looking at the past exam with Question 1 - I understand the state space and how to portray it (like in 1.2 the first answer).

I can't seem to wrap my brain around the second notation however:

Quote

f3 : if 3< T then (3, F)
f5 : if 5< F then (T, 5)
e3 : if 0> T then (0, F)
e5 : if 0> F then (T, 0)
p3,5: if (5-F)<=T then (T-(5-F),5) else (0,T+F)
p5,3: if (3-T)<=F then (3,F-(3-T)) else (T+F,0)

Anyone got some clarity, no matter how I convert it to english, I end up sounding wrong.

As far as I understand it:
(T,F) represents the amount of water in the Three and Five liter jugs respectively
So (1,2) means there is 1l in the 3l jug and 2l in the 5l jug.

f3 : if T < 3 then (3,F)

Filling up the 3l jug will mean T=3 and F=F (unchanged)

f5 : if F < 5 then (T,5)

Filling up the 5l jug will mean F=5 and T=T (unchanged)

e3 : if T > 0 then (0,F)
e5 : if F > 0 then (T,0)

Emptying either jug will mean T or F = 0 leaving the other unchanged.

p3,5: if (5-F)<=T then (T-(5-F),5) else (0,T+F)
p5,3: if (3-T)<=F then (3,F-(3-T)) else (T+F,0)

This is where I think it gets a bit confusing, this is taking into account an "overflow" so if T=3 and F=3, T can only pour 2l into F leaving 1l in T, else T will be emptied and F will just have it's amount increased by T.
It's similar for pouring from F to T.

I think I'm just going to go with the 6 marks. That notation just makes no sense to me (it's the <'s that catch me out). Shot for the reply tho.