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Relations Test 3

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Relations Test 3
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  • Question 1
    1 / -0
    If xx and yy coordinate of a point is (3,10)(3, 10), then the xx co-ordinate is
    Solution
    Here, xx co-ordinate will be the first entry in ordered pair.
    So, option B is correct.
  • Question 2
    1 / -0
    If xx and yy co-ordinate of a point is (3,10)(3, 10), then yy co-ordinate is
    Solution
    yy coordinate will be second entry in ordered pair.
    So, option C is correct.
  • Question 3
    1 / -0
    The first component of all ordered pairs is called
    Solution
    The first components of all order pair is called Domain.
    The second components of all ordered pair is called Range.
  • Question 4
    1 / -0
    If aa and bb are two variables and (a,b)=(b,a)(a, b)=(b, a), then 
    Solution
     (a,b)=(b,a)(a, b) = (b, a) only if a=b.a = b..
    So, option C is correct.
  • Question 5
    1 / -0
    Which of the ordered pair satisfies the relation x<yx<y?
    Solution
    (A) (1,2)(A)  (1,2)
    x<yx<y
    1<21<2
    True , x<yx<y

    (B)(2,1)(B) (2,1)
    2>12>1

    (C)(1,1)(C) (1,1)
    x=yx=y

  • Question 6
    1 / -0
    If yy is second entry and xx is first entry then its ordered pair will be ............
    Solution
    If xx is first entry and yy is second, then its ordered pair will be (x,y)(x, y).

    So, option A is correct.
  • Question 7
    1 / -0
    What is general representation of ordered pair for two variables aa and bb?
    Solution
    An ordered pair is written in the form (x(x-coordinate, yy-coordinate)).
  • Question 8
    1 / -0
    Ordered pairs (x,y)(x, y) and (1,1)(-1, -1) are equal if y=1y = -1 and x=x = _____
    Solution
    Given , (xy)=(1,1)(x-y)=(-1,1)
    x=1,y=1x=-1, y=-1
    The value of x=1x=-1.
  • Question 9
    1 / -0
    Let A={1,2,3}A = \left \{1, 2, 3\right \}. Then number of equivalence relations containing (1,2)(1, 2) is

    Solution
    Total possible pair={(1,1),(1,2),(1,2),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)}\{ (1,1),(1,2),(1,2),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\}
    Reflexive means (a,a)(a,a) should be in relation.
    So,(1,1),(2,2),(3,3)(1,1),(2,2),(3,3) should be in relation.
    Symmetric means if (a,b)(a,b) is in relation,then (b,a)(b,a) should be in relation.
    So,since (1,2)(1,2) is in relation (2,1)(2,1) should also be in relation.
    Transitive means if (a,b)(a,b) is in relation and (b,c)(b,c) is in relation.
    So if (1,2)(1,2) is in relation and (2,1)(2,1) is in relation,then (1,1)(1,1) should be in relation.
    Relative R1={(1,2),(1,1),(2,2),(3,3),(2,1)}R1=\{ (1,2),(1,1),(2,2),(3,3),(2,1)\}
    So,smallest relation is R1={(1,2),(2,1),(1,1),(2,2),(3,3)}R1=\{(1,2),(2,1),(1,1),(2,2),(3,3)\}
    If we add (2,3)(2,3) ,then we have to add (3,2)(3,2) also,as it is symmetric but as (1,2)&(2,3)(1,2)\&(2,3) are there,we need to add (1,2)(1,2) also,as it is transitive.
    As we are adding (1,3)(1,3) we should add (3,1)(3,1) also,as it is symmetric.
    Relation R2={(1,2),(2,1),(1,1),(2,2),(3,3),(2,3),(1,3),(3,1)}R2=\{(1,2),(2,1),(1,1),(2,2),(3,3),(2,3),(1,3),(3,1)\}
    Hence only two possible relation are there which are equivalence.
  • Question 10
    1 / -0
    Find the second component of an ordered pair (2,3)(2, -3)
    Solution
    In an ordered pair (x,y)(x,y), the first component is xx and the second component is yy.
    Therefore, in an ordered pair (2,3)(2,-3), the second component is 3-3.
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