Let $A_1, A_2, \ldots, A_6$ are six sets, each with four elements and $B_1, B_2, \ldots ., B_n$ are $n$ sets, each with two elements. Let $S=A_1 \cup A_2 \cup \ldots \cup A_6=B_1 \cup B_2 \cup \ldots \cup B_n$.

Given that each element of $S$ belongs to exactly four of the A's and to exactly three of the B's. Then $n$ is

The number of reflexive relations on a set $A$ of $n$ elements is equal to

In R, a relation p is defined as follows: $$\forall a, b \in \mathbb{R}, a p$$ holds iff $$a^2-4 a b+3 b^2=0$$. Then

Let A be the set of even natural numbers that are < 8 & B be the set of prime integers that are $$<7$$ The number of relations from A to B are