This can be solved using overlapping sets method

AUBUC = A+B+C- (exactly 2)-2(all three) + Neither

Neither =0 as each student read atleast 1 proposal
A= 38, B=36, C=28
50= 102 -(exactly 2)-2(all three)
(exactly 2) +2 (all three) = 52

Let exactly 2= x
all three =y

x+2y = 52
Required least value of x+y

x+y= 52-y

we can see that x+y will be minimum when y is maximum. to get the maximum value of y we have to make x=0, thus
2y=52
or y=26
Thus the required value of x+y will be
x+y = 52-26 =26