Question

1. Fill in the blanks in each of the following:

(a) If A and B are two finite sets, then n(A) + n(B) is equal to ___________

(b) If A is a finite set containing n element, then number of subsets of A is _______.

(c) The set {x ∈ R : 1 ≤ x < 2} can be written as ______________.

(d) When A = φ, then number of elements in P(A) is ______________.

(e) When A = φ, then number of elements in P(P(P(A))) is ______________.

(f) If A and B are finite sets such that A ⊂ B, then n (A ∪ B) = ______________.

(g) Power set of the set A = {1, 2, -1} is ______________.

(h)Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set

of all the three sets A, B and C can be ______________.

2. State whether the following statements are True or False.

(a) Let R and S be the sets defined as follows:

R = {x ∈ Z | x is divisible by 2}, S = {y ∈ Z | y is divisible by 3}, then R ∩ S = φ

(b) Q ∩ R = Q, where Q is the set of rational numbers and R is the set of real numbers.

(c) If A is any set, then A ⊂ A

(d) Given that A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ A

(e) The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.

(f) The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equivalent.

(g) A ∪ B = A, where A is the set of rational numbers and B is the set of integers.

(h) Let sets A and B be defined as A = {x ∈ Z | x is divisible by 2},

B = {x ∈ Z | x is divisible by 6}. Then B ⊂A

(i) Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B​

Answer 1

1. if a and b are both infinite