16. Which of the following sets is empty?

1. 1. A = {x: x ∈ n and x ≤ 1}
      

   
   
   

   2. B = {x: 3x + 1 = 0, x ∈ N}

   
   
   

   3. C = {x: x is an integer and -1 < x < 1}

   
   
   

   4. D = set of months of the year beginning with F.
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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17. Find the cardinal number of the following set {x: x is a natural number ≤ 30 and is divisible by 7 or 11}
    

1. 1. 4

   
   
   

   2. 8

   
   
   

   3. 6

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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18. For which of the following cases A and B are equivalent?

1. 1. A = {a, b, c,…, z}, B = {1, 2, 3,…, 24}

   
   
   

   2. A = {1/3,1/2,3/5}, B = { x : x = n/n+2, n ε N}

   
   
   

   3. A = {2, 4, 6}, B = {(2, 4), (4, 6), (2, 6)}

   
   
   

   4. A = { x : x = ( n³ - 1 )/ ( n³ + 1) , n ε W, n ≤ 3} , B = { 0,7/9,13/14}
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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19. Write down the power set of the set {0}.

1. 1. ϕ

   
   
   

   2. {0}

   
   
   

   3. {ϕ}

   
   
   

   4. {ϕ, {0}}
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let, A = {0}. The possible subsets of this set A are Φ and {0}.

   Correct Option: D

   Let, A = {0}. The possible subsets of this set A are Φ and {0}, so the power set of the given set A is P(A) = {f, {0}}.

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20. Let A = {ϕ, {ϕ}, 1, {1, ϕ}, 7}. Which of the following is false?

1. 1. ϕ ∈ A
      

   
   
   

   2. {ϕ} ∈ A

   
   
   

   3. {1} ∈ A

   
   
   

   4. {7, ϕ,} ⊂ A

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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