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I.Sc (Math)

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39 Questions
Home/Class 12/I.Sc (Math)/Page 2
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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by

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R = {(a, b) : |a – b| is a multiple of 4} R = {(a, b) : a = b}

  1. R = {(a, b) : |a – b| is a multiple of 4}
  2. R = {(a, b) : a = b}
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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a – b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive.

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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Determine whether each of the following relations are reflexive, symmetric and transitive:

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Relation R in the set A = {1, 2, 3, …, 13, 14} defined as R = {(x, y) : 3x – y = 0} Relation R in the set N of natural numbers defined as R = {(x, y) : ...Read more

  • Relation R in the set A = {1, 2, 3, …, 13, 14} defined as
    R = {(x, y) : 3x – y = 0}
  • Relation R in the set N of natural numbers defined as
    R = {(x, y) : y = x + 5 and x < 4}
  • Relation R in the set A = {1, 2, 3, 4, 5, 6} as
    R = {(x, y) : y is divisible by x}
  • Relation R in the set Z of all integers defined as
    R = {(x, y) : x – y is an integer}
  • Relation R in the set A of human beings in a town at a particular time given by
  1. R = {(x, y) : x and y work at the same place}
  2. R = {(x, y) : x and y live in the same locality}
  3. R = {(x, y) : x is exactly 7 cm taller than y}
  4. R = {(x, y) : x is wife of y}
  5. R = {(x, y) : x is father of y}
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Query KaroQK#001
Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive.

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