Sets Set 2

From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is

Let be the non-void set of the children in a family. The relation is a brother of on is

In a class of 30 pupils 12 take needls work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is

If is a relation on a finite set having elements, then the number of relations on is

The void relation on a set is

Suppose are thirty sets, each having 5 elements and are sets each with 3 elements, let
 and each element of  belongs to exactly 10 of the  and exactly 9 of the .
Then, n is equal to

If is a finite set having elements, then has

Let and have 3 and 6 elements respectively. What can be the minimum number of elements in ?

Let be a reflexive relation on a set and be the identity relation on Then,

If are sets such that and then