Let z = [y] and y = [x] − x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z ?

If A = {{1, 2, 3}}, then how many elements are there in the power set of A?

Consider all the subsets of the set A = {1, 2, 3, 4}. How many of them are supersets of the set {4}?

Consider the following statements in respect of two non-empty sets A and B :

1. x ∉ (A ∪ B) ⇒ x ∉ A or x ∉ B

2. x ∉ (A ∩ B) ⇒ x ∉ A and x ∉ B

Which of the above statements is/are correct?