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Venn Diagrams & Set Theory Test - 6
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Venn Diagrams & Set Theory Test - 6
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  • Question 1/10
    3 / -1

    Let R be a non-empty relation on a collection of sets defined by ARB if and only if A  ∩ B = Ø
    Then (pick the TRUE statement) 

    Solutions

    The correct answer is B asLet A={1,2,3
    B={4,5} 
    C={1,6,7}
    now 
    A∩B=∅ 
    B∩C=∅
    B∩C=∅ but 
    A∩C≠∅
    R is not transitive.

    A∩A=A
    R is not reflexive.

    A∩B=B∩A
    R is symmetric
    So, 
    A is false as 
    R is not reflexive or transitive
    B is true.
    C is false because 
    R is not transitive or reflexive
    D is false because 
    R is symmetric
     

  • Question 2/10
    3 / -1

    The binary relation S =  Φ (empty set) on set A = {1, 2,3}  is

    Solutions

    Explanation:

    • Reflexive : A relation is reflexive if every element of set is paired with itself. Here none of the element of A is paired with themselves, so S is not reflexive.
    • Symmetric : This property says that if there is a pair (a, b) in S, then there must be a pair (b, a) in S. Since there is no pair here in S, this is trivially true, so S is symmetric.
    • Transitive : This says that if there are pairs (a, b) and (b, c) in S, then there must be pair (a,c) in S. Again, this condition is trivially true, so S is transitive.

      Thus, option (D) is correct.

  • Question 3/10
    3 / -1

    Which of the following sets are null sets ?

    Solutions

    There are some sets that do not contain any element at all. For example, the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } or Ø.

  • Question 4/10
    3 / -1

    Number of subsets of a set of order three is

    Solutions

    Number of subset = 2n
    order 3 = 23
    ⇒ 8

  • Question 5/10
    3 / -1

    "n/m" means that n is a factor of m, then the relation T is

    Solutions

    ′/′ is reflexive since every natural number is a factor of itself that in n/n for n∈N.
    ′/′ is transitive if n is a factor of m and m is a factor of P, then n is surely a factor of P.
    However, ′/′ is not symmetric.
    example, 2 is a factor of 4 but 4 is not a factor of 2. 

  • Question 6/10
    3 / -1

    The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is

  • Question 7/10
    3 / -1

    If A and B are sets and A∪ B= A  ∩ B, then

  • Question 8/10
    3 / -1

    Let S be an infinite set and S1, S2, S3, ..., Sn be sets such that S1 ∪S2 ∪S3∪ .......Sn = S then

    Solutions

    Let S = S1 ∪ S2 ∪ S3 ∪ .... Sn . 
    For S to be infinite set, atleast one of sets Si must be infinite, 
    if all Si were finite, then S will also be finite.

  • Question 9/10
    3 / -1

    If X and Y are two sets, then X  ∩ (Y  ∪ X) C equals

    Solutions

  • Question 10/10
    3 / -1

    If  f : X -> Y and a, b  ⊆ X, then f (a  ∩ b) is equal to

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