The maximum number of equivalence relations on the set A = {3, 5, 7}

The correct answer is Option (4) → 5

For the set A = {3, 5, 7}, we have n = 3. The bell numbers for small values of n are:

$B_1=1,B_2=2,B_3=5$

Thus, the maximum no. of equivalence relation is,

$B_3=5$