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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) }

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  1. If A and B have n elements in common, how many elements do A × B and B × A have in common?
    1. n
    2. n3
    3. n2
    4. None of these
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    NA

    Correct Option: C

    NA

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  1. If U = {a, b, c, d, e, f}, A = {a, b, c}, B = {c, d, e, f}, C = {c, d, e}, find (A ∩ B) ∪ (A ∩ C).
    1. {c}
    2. {a}
    3. {b}
    4. {d}
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    A ∩ B = { a, b, c } ∩ { c, d, e, f }
    A ∩ C = { a, b, c } ∩ { c, d, e }

    Correct Option: A

    A ∩ B = {a, b, c} ∩ {c, d, e, f}
    A ∩ B = { c }
    A ∩ C = { a, b, c } ∩ { c, d, e }
    A ∩ C = { c }
    ∴ (A ∩ B) ∪ (A ∩ C) = { c }.

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  1. If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ∪ A)′.
    1. U
    2. A
    3. Φ
    4. None of these
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    U ∪ A = {a, b, c, d, e, f} ∪ {a, b, c}

    Correct Option: C

    U ∪ A = {a, b, c, d, e, f} ∪ {a, b, c} = {a, b, c, d, e, f} = U
    (U ∪ A)′ = Φ.

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  1. Let A = {1, 3, 5} and B = {x: x is an odd natural number < 6}. Which of the following is false?
    1. A ⊂ B
    2. B ⊂ A
    3. A = B
    4. None of these
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    NA

    Correct Option: D

    NA

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