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Sets and Functions

  1. If P = { 1, 2, 3 } and Q = { 4 , 5 } then what is the value of P × Q ?
    1. { (4 , 5) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
    2. { (1 , 4) , (4 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
    3. { (1 , 4) , (1 , 5) , (2 , 4) , (3 , 5) , (3 , 4) , (3 , 5) }
    4. { (1 , 4) , (1 , 5) , (2 , 4) , (2 , 5) , (2 , 4) , (3 , 5) }
    5. { (1 , 4) , (1 , 5) , (2 , 4) , (2 , 5) , (3 , 4) , (3 , 5) }
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    Use the the Cartesian product X × Y formula.
    The Cartesian product X × Y of sets X , Y is the set of all ordered pairs ( x , y ).
    Two ordered pairs ( x1 , y1 ), ( x2 , y2 ) .

    Correct Option: E

    The Cartesian product X × Y of sets X , Y is the set of all ordered pairs ( x , y ).
    Two ordered pairs ( x1 , y1 ), ( x2 , y2 ) .
    Given that P = { 1, 2, 3 } and Q = { 4 , 5 } then,
    P x Q = { 1, 2, 3 } x { 4 , 5 }
    P x Q = { 1 } x { 4 , 5 } , { 2 } x { 4 , 5 } , { 3 } x { 4 , 5 }
    P x Q = { 1 , 4 } , { 1 , 5 } , { 2 , 4 } , { 2 , 5 } , { 3 , 4 }, { 3 , 5 }
    P x Q = { (1 , 4 ) , ( 1 , 5 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 3 , 4 ), ( 3 , 5) }

    Report

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