# Working of ForAll [closed]

Reduce[{qwin == hwin*awin*(tr - ta), qleak == ql*tr, qheat < 50000, ql > 0, qheat > 0, tr > 22, tr < 25, qheat == qleak + qwin + cp*(tr - ta), cp == 1.4, ta == 10, awin == 20, hwin > 100, hwin < 1000}, {qwin, tr, ta, ql, awin, qleak, qheat, cp, hwin}, Reals]


The above result has feasible solution when hwin is between 120 and 150. However if I use ForAll, it is showing the opposite

Reduce[ForAll[hwin, hwin > 120 && hwin < 150, And[qwin == hwin*awin*(tr - ta), qleak == ql*tr, qheat < 50000, ql > 0, qheat > 0, tr > 22, tr < 25, qheat == qleak + qwin + cp*(tr - ta), cp == 1.4, ta == 10, awin == 20, hwin > 100, hwin < 1000]], Reals]


Am I missing something?

• Do you have any values associated with your variables? The results of evaluation of your expression are distinctly more complicated than you seem to imply. – MarcoB Apr 14 '16 at 4:21
• @MarcoB I have given all the constraints on my variables as equations. The result of Reduce shows that hwin depends on awin, tr,qwin and ta. Out of those ta & awin are constants. Further, using the limits on qwin & tr, I concluded that hwin varies from 100 to around 208. – Prashanth Apr 14 '16 at 4:36