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数学表达式: 从恐惧到单挑-作业day2

作者:互联网

4.6 作业

  1. 令 A = { 1 , 2 , 5 , 8 , 9 } \mathbf{A} = \{1, 2, 5, 8, 9\} A={1,2,5,8,9}, 写出 A \mathbf{A} A 上的 “模 2 同余” 关系及相应的划分.
    答: R = { ( a , b ) ∈ A × A ∣ a m o d    2 = b m o d    2 } . \mathbf{R} = \{(a, b) \in \mathbf{A} \times \mathbf{A} \vert a \mod 2 = b \mod 2\}. R={(a,b)∈A×A∣amod2=bmod2}.
            \space\space\space\space\space\space\space         R = { ( 1 , 5 ) , ( 1 , 9 ) , ( 2 , 8 ) , ( 5 , 9 ) } . \mathbf{R} = \{(1,5),(1,9),(2,8),(5,9)\}. R={(1,5),(1,9),(2,8),(5,9)}.
            \space\space\space\space\space\space\space         P = { { 1 , 5 , 9 } , { 2 , 8 } } . \mathcal{P} = \{\{1,5,9\},\{2,8\}\}. P={{1,5,9},{2,8}}.
  2. A = { 1 , 2 , 5 , 8 , 9 } \mathbf{A} = \{1, 2, 5, 8, 9\} A={1,2,5,8,9},自己给定两个关系 R 1 \mathbf{R}_1 R1​和 R 2 \mathbf{R}_2 R2​, 并计算 R 1 R 2 \mathbf{R}_1 \mathbf{R}_2 R1​R2​, R 1 + \mathbf{R}_1^+ R1+​, R 1 ∗ \mathbf{R}_1^* R1∗​.
    答: R 1 = { ( 1 , 2 ) , ( 5 , 8 ) } \mathbf{R}_1=\{(1, 2), (5, 8)\} R1​={(1,2),(5,8)}, R 2 = { ( 2 , 9 ) , ( 5 , 9 ) , ( 1 , 8 ) } \mathbf{R}_2=\{(2, 9), (5, 9),(1,8)\} R2​={(2,9),(5,9),(1,8)}
            \space\space\space\space\space\space\space         R 1 R 2 = { ( 1 , 9 ) } \mathbf{R}_1 \mathbf{R}_2=\{(1,9)\} R1​R2​={(1,9)}
            \space\space\space\space\space\space\space         R 1 + = ⋃ i = 1 ∣ A ∣ R 1 i = ⋃ i = 1 5 R 1 i \mathbf{R}_1^+=\bigcup_{i = 1}^{|\mathbf{A}|} \mathbf{R}_1^i=\bigcup_{i = 1}^5\mathbf{R}_1^i R1+​=⋃i=1∣A∣​R1i​=⋃i=15​R1i​
            \space\space\space\space\space\space\space                 \space\space\space\space\space\space\space         = R 1 ∪ R 1 R 1 ∪ R 1 R 1 R 1 ∪ R 1 R 1 R 1 R 1 ∪ R 1 R 1 R 1 R 1 R 1 =\mathbf{R}_1\cup\mathbf{R}_1\mathbf{R}_1\cup\mathbf{R}_1\mathbf{R}_1\mathbf{R}_1\cup\mathbf{R}_1\mathbf{R}_1\mathbf{R}_1\mathbf{R}_1\cup\mathbf{R}_1\mathbf{R}_1\mathbf{R}_1\mathbf{R}_1\mathbf{R}_1 =R1​∪R1​R1​∪R1​R1​R1​∪R1​R1​R1​R1​∪R1​R1​R1​R1​R1​
                   \space\space\space\space\space\space\space\space\space\space\space\space\space\space                = { ( 1 , 2 ) , ( 5 , 8 ) } ∪ ∅ ∪ ∅ ∪ ∅ ∪ ∅ =\{(1, 2), (5, 8)\}\cup\emptyset\cup\emptyset\cup\emptyset\cup\emptyset ={(1,2),(5,8)}∪∅∪∅∪∅∪∅
                   \space\space\space\space\space\space\space\space\space\space\space\space\space\space                = { ( 1 , 2 ) , ( 5 , 8 ) } =\{(1, 2), (5, 8)\} ={(1,2),(5,8)}
            \space\space\space\space\space\space\space         R 1 ∗ = R + ∪ A 0 \mathbf{R}_1^*= \mathbf{R}^+ \cup \mathbf{A}^0 R1∗​=R+∪A0
            \space\space\space\space\space\space\space         A 0 = { ( x , x ) ∣ x ∈ A } = { ( 1 , 1 ) , ( 2 , 2 ) , ( 5 , 5 ) , ( 8 , 8 ) , ( 9 , 9 ) } \mathbf{A}^0 = \{(x, x) \vert x \in A\}=\{(1,1),(2,2),(5,5),(8,8),(9,9)\} A0={(x,x)∣x∈A}={(1,1),(2,2),(5,5),(8,8),(9,9)}
            \space\space\space\space\space\space\space         R 1 ∗ = { ( 1 , 2 ) , ( 5 , 8 ) , ( 1 , 1 ) , ( 2 , 2 ) , ( 5 , 5 ) , ( 8 , 8 ) , ( 9 , 9 ) } \mathbf{R}_1^*=\{(1, 2), (5, 8),(1,1),(2,2),(5,5),(8,8),(9,9)\} R1∗​={(1,2),(5,8),(1,1),(2,2),(5,5),(8,8),(9,9)}

标签:mathbf,R1,R2,space,单挑,cup,day2,emptyset,表达式
来源: https://blog.csdn.net/qq_33287070/article/details/119140669