For what value of θ, where 0 < θ < $\frac{\pi}{2}$, does sin θ + sin θ cos θ maximum value?

Consider the following statements in respect of sets:

1. The union over the intersection of sets is distributive.

2. The complement of the union of two sets is equal to the intersection of their complements.

3. If the difference between the two sets is equal to the empty set, then the two sets must be equal.

Which of the above statements are correct?

Consider three sets X, Y and Z having 6, 5 and 4 elements respectively. All these 15 elements are distinct. Let S = (X - Y) ∪ Z. How many proper subsets does S have?

Consider the following statements in respect of relations and functions:

1. All relations are functions but all functions are not relations.

2. A relation from A to B is a subset of Cartesian product A × B.

3. A relation in A is a subset of Cartesian product A × A.

Which of the above statements are correct?