Sets

If S is the set of distinct values of 'b' for which

If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is:

an empty set
an infinite set
a finite set containing two or more elements
a singleton

If X = {4^n - 3n -1 : n ∈ N} and Y = {9(n - 1) : n ∈ N}

If X = {4ⁿ - 3n -1 : n ∈ N} and Y = {9(n - 1) : n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to

Y
Y - X
X
N

Let A and B be two sets containing four and two elements respectively

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is

If A, B and C are three sets such that

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

B = C
A = C
A ∩ B = φ
A = B