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Relations Test 4

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Relations Test 4
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Weekly Quiz Competition
  • Question 1
    1 / -0
    The second component of all ordered pairs of a relation is
    Solution
    The second components of all ordered pairs of a relation is Range.
  • Question 2
    1 / -0
    A ______ maps elements of one set to another set.
    Solution
    A relation map elements of one set to another set
    R:ABR:A\to B
    Elements in A is mapped to elements in set B.
  • Question 3
    1 / -0
    The ______ product of two sets is the set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set.
    Solution
    The cartesian product of two sets is the set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set. 
    Example:A={1,2}B={2} A = \{1, 2\} \quad B = \{2\}
    cartesian product, A×B=(1,2),(2,2)A \times B = {(1,2), (2, 2)}
  • Question 4
    1 / -0
    Identify the first component of an ordered pair (2,1)(2, 1).
    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 (2,1)(2,1), the first component is 22.
  • Question 5
    1 / -0
    Cartesian product of sets AA and BB is denoted by _______.
    Solution
    Cartesian product of Set AA and BB is denoted by A×BA\times B.
  • Question 6
    1 / -0
    What is the relation for the statement "A is taller than B"?
    Solution
    A is taller than B.
    A is related to B by 'taller than'.
  • Question 7
    1 / -0
    Identify the first component of an ordered pair (0,1)(0, -1) .
    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 (0,1)(0,-1), the first component is 00.
  • Question 8
    1 / -0
    If A={1,2,3},B={3,4}A = \{1, 2, 3\}, B = \{3, 4\}
    find (A ×\times B) \cup (B ×\times A)
    Solution
    (A×B)={(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)} (A\times B) = \left \{ (1,3),(1,4),(2,3),(2,4),(3,3),(3,4) \right \}
    (B×A)={(3,1),(3,2),(3,3),(4,1),(4,2),(4,3)} (B\times A) = \left \{ (3,1),(3,2),(3,3),(4,1),(4,2),(4,3) \right \}
    (A×B)(B×A)={(1,3),(1,4),(2,3),(2,4),(3,3),(3,4),(3,1),(3,2),(4,1),(4,2),(4,3)} \Rightarrow (A\times B)\cup (B\times A)= \left \{ (1,3),(1,4),(2,3),(2,4),(3,3),(3,4),(3,1),(3,2),(4,1),(4,2),(4,3) \right \}  
  • Question 9
    1 / -0
    If A= {0, 1} and B ={1, 0}, then what is A x B equal to ?
    Solution
    {0,1}×{1,0}={(0,1),(0,0),(1,1),(1,0)} \left\{ { 0,1 } \right\} \times \left\{ 1,0 \right\} ={ \left\{ (0,1),(0,0),(1,1),(1,0) \right\}  }
    {0,1}×{0,1}={(0,0),(0,1),(1,0),(1,1)} \left\{ { 0,1 } \right\} \times \left\{ 0,1 \right\} ={ \left\{ (0,0),(0,1),(1,0),(1,1) \right\}  }

    So, A×B=A×AA\times B=A\times A
    Hence, D is correct.
  • Question 10
    1 / -0
    If A={a,b},B={1,2,3}A = \{a, b\}, B=\{1, 2, 3\}, find B ×\times A
    Solution
    To find B × A multiply each element of B with that of A & form an ordered pair.
     i.e. ordered pairs are (1,a); (2,a); (3,a); (1,b); (2,b); (3,b)
    Therefore B × A = {  (1,a), (2,a), (3,a), (1,b), (2,b), (3,b)}
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