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I.Q. Tests
 

 

˹á | ѡ¹ | ˹áԵʵ | ٵäԵʵ

ٵäԵʵ
   

૵ (Sets)
 



  1. ૵ӡѴ ૵ըӹǹҪԡ繨ӹǹǡ ٹ

    A = {1, 2, 3, 4} ¶֧ ૵ A ըӹǹҪԡ 4 ѧ ૵ A ૵ӡѴ

    B = {x l x N 1 < x < 2} ¶֧ ૵ B Ҫԡ 0 ѧ ૵ B ૵ӡѴ


  2. ૵͹ѹ ૵öѺӹǹҪԡ繨ӹǹǡ͹ (ըӹǹҪԡҡ)

    A = {1, 2, 3, 4, ...} ¶֧ ૵ A Ҫԡ繨ӹǹѺҡ¹Ѻǹ騺

    B = {x l x Q 0 < x < 5} ¶֧ ૵ B Ҫԡ繨ӹǹá (շ駨ӹǹӹǹҡ¹Ѻǹ)


  3. ૵ҧ ૵ըӹǹҪԡ ૵ըӹǹҪԡҡѺٹ

    A = { }

    B = {x l x N x < 1}




  1. ẺᨡᨧҪԡ

    A = {1, 2, 3, 4, ...}

    B = {x, y, z}


  2. Ẻ͡͹

    A = {x l x I X - 5 = 0}

    B = {x l x 繪ͧ͢ѹ 1 ѻ}




  1. ૵ҡѹ (Equal sets)

    ૵ҡѹͧ૵ еͧ૵͹ѹء ¹᷹ѭѡɳ A = B

    A = {1, 2, 3} B = {2, 1, 1, 3}

    A = B


  2. ૵ºҡѹ (Equivalent sets)

    ૵ͧ૵ ͧӹǹҪԡҡѹ ¹᷹ѭѡɳ A ↔ B

    A = {x, y, z}

    B = {1, 2, 3}

    A ↔ B




૵ A Ѻ૵ͧ૵ B ҪԡءǢͧ૵ A Ҫԡͧ૵ B ¹᷹ѭѡɳ A B ѭѡɳ "Ѻ૵"

A = {a, b, c} B = {a, b, c ,d}

A B B A


    Ѻ૵

    A B A ≠ B ѧҧ ¡ A Ѻ૵ͧ B


    ҨӹǹѺ૵

    ૵ A ૵ӡѴ Ҫԡ n

      ӹǹѺ૵ͧ A = 2n

    ͤè ૵ҧ (Ø) Ѻ૵ͧء ૵


    ѵԢͧѺ૵

    ˹ A, B C ૵

    1. A A


    2. Ø A


    3. A = B B = A


    4. A B B C A C


    5. A = B A B B A




ôԹǡѺ૵ 繡ôԹҧ૵ҡ૵˹ 4 Ẻ

  1. ¹ (Union)

    ¹ͧ૵ A ૵ B ૵ҪԡҪԡͧ૵ A ૵ B

    ͧͧ૵ ¹᷹ѭѡɳ A B

      蹤 A B = {x l x A x B x Ҫԡͧͧ૵}

      A = {0, 1, 2, 3} B = {1, 3, 5, 7}

      A B = {0, 1, 2, 3, 5, 7}


  2. Թૡѹ (Intersection)

    Թૡѹͧ૵ A ૵ B ૵ҪԡҪԡͧ૵ A ૵ B

    ¹᷹ѭѡɳ A ∩ B

      蹤 A ∩ B = {x l x A x B}

      A = {0, 1, 2, 3} B = {0, 3, 5}

      A ∩ B = {0, 3}


  3. (Complement)

    ˹૵ A Ѻ૵ͧ͡ѷ

    ͧ૵ A ૵СͺҪԡҪԡͧ Ҫԡͧ૵ A ¹᷹ѭѡɳ A'

      蹤 A' = {x l x x A}

      = {0, 1, 2, 3, 4} , A = {0, 2, 4} B = {3, 4}

      A' = {1, 3}

      B' = {0, 1 ,2}


  4. ŵҧ (Difference)

    ŵҧҧ ૵ A ૵ B ¶֧ ૵Ҫԡ૵ A ૵ B
    ¹᷹ѭѡɳ A - B
    ŵҧҧ ૵ B ૵ A ¶֧ ૵Ҫԡ૵ B ૵ A
    ¹᷹ѭѡɳ B - A

      蹤 A - B ={x l x A x B}

      B - A = {x l x B x A}

      A = {0, 1, 2, 3, 4} B = {3, 4, 5, 6, 7}

      A - B = {0, 1, 2}

      B - A = {5, 6, 7}



૵ ૵ͧѺ૵ ¹᷹ѭѡɳ P(A)

    蹤 P(A) = {x l x A}

    A = {1, 2, 3}

    P(A) = {Ø, {1} , {2} , {3} , {1, 2} , {1, 3} , {2, 3} , {1, 2, 3}}

    ѵԢͧ૵

    ˹ A B ૵

    1. Ø P(A)


    2. Ø P(A)


    3. A P(A)


    4. A ૵ӡѴ A Ҫԡ n P(A) Ҫԡ 2n


    5. A B P(A) P(B)


    6. P(A) ∩ P(B) = P(A ∩ B)


    7. P(A) P(B) P(A B)



    ó 2 ૵

      n(A B) = n(A) + n(B) - n(A ∩ B)


    ó 3 ૵

      n(A B C) = n(A) + n(B) + n(c) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C)


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