Question

1. Fill in the blanks in each of the following: <br /><br />(a) If A and B are two finite sets, then n(A) + n(B) is equal to ___________<br /><br />(b) If A is a finite set containing n element, then number of subsets of A is _______.<br /><br />(c) The set {x ∈ R : 1 ≤ x < 2} can be written as ______________.<br /><br />(d) When A = φ, then number of elements in P(A) is ______________.<br /><br />(e) When A = φ, then number of elements in P(P(P(A))) is ______________.<br /><br />(f) If A and B are finite sets such that A ⊂ B, then n (A ∪ B) = ______________.<br /><br />(g) Power set of the set A = {1, 2, -1} is ______________.<br /><br />(h)Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set <br /><br />of all the three sets A, B and C can be ______________.<br /><br />2. State whether the following statements are True or False.<br /><br />(a) Let R and S be the sets defined as follows:<br /><br /> R = {x ∈ Z | x is divisible by 2}, S = {y ∈ Z | y is divisible by 3}, then R ∩ S = φ<br /><br /> (b) Q ∩ R = Q, where Q is the set of rational numbers and R is the set of real numbers.<br /><br /> (c) If A is any set, then A ⊂ A <br /><br /> (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<br /><br /> (e) The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.<br /><br /> (f) The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equivalent. <br /><br /> (g) A ∪ B = A, where A is the set of rational numbers and B is the set of integers.<br /><br /> (h) Let sets A and B be defined as A = {x ∈ Z | x is divisible by 2},<br /><br /> B = {x ∈ Z | x is divisible by 6}. Then B ⊂A<br /><br /> (i) Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B​

Answer 1

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Answer 2

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