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?

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

1. A ∪ B = A ∩ B if A = B

2. A Δ B = ϕ  if A = B

Which of the above statements is/are correct ?