Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if x² - 5xy + 4y² = 0 :

1. R is reflexive

2. R is symmetric

3. R is transitive

Which of the above statements is /are correct ?

Consider the following statements in respect of any relation R on a set A :

1. If R is reflexive, then R^-1 is also reflexive

2. If R is symmetric, then R^-1 is also symmetric

3. If R is transitive, then R^-1 is also transitive

Which of the above statements are correct?

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?