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Linear Algebra |

Linear Algebra |

Last update 

The Basics of Alliments and Co! -Set Theory

Items (47)

  • A⊂B

    A⊆B ∧ A ≠ B

  • A⊆B

    ∀x (x∈A ⇒ x∈B)

  • Cardinality: |A|

    Number of distinct elements in A

  • Cartesian Product: A x B

    {(a,b) | a ∈ A ∧ b ∈ B}

  • A∪B

    {x | x∈A ∨ x∈B}

  • A∩B

    {x | x∈A ∧ x∈B}

  • A\B

    {x | x∈A ∧ x∉B}

  • A{1,3,4,7}, B{4,1,3,7}, A⊆B? A⊂B?

    Yes No

  • A{1,3,4,7}, B{4,1,3,2,7}, A⊆B? A⊂B?

    Yes Yes

  • A{1,3,8,4,7}, B{4,1,3,5,2,7}, A⊆B? A⊂B?

    No, No

  • A{1,2,3}, B{2,1,3,4,6}, A⊆B? A⊂B?

    Yes Yes

  • A{1,2,3}, B{3, 3, 4}, |A|? |B|?

    (3) (2)

  • A{1,2}, B{2, 3, 4}, A x B?

    {(1,2),(1,3),(1,4),(2,2),(2,3),(2,4)}

  • A{1,3}, B{2,4}, A x B?

    {(1,2),(1,4),(3,2),(3,4)}

  • A{1,3}, B{2,4}, B x A?

    {(2,1),(2,3),(4,1),(4,3)}

  • A{1,3}, B{2,4}, |B x A|?

    4

  • A{1,2}, B{2, 3, 4}, |A x B|?

    6

  • A{1,2}, B{2, 3, 4}, A ∪ B?

    {1,2,3,4}

  • A{1,2}, B{2, 3, 4}, A ∩ B?

    {2}

  • A{1,2}, B{2, 3, 4}, |A ∪ B|?

    4

  • A{1,2}, B{2, 3, 4}, |A ∩ B|?

    1

  • A{1,2,3}, B{2,1,4,6}, A\B?

    {3}

  • A{1,2,3}, B{2,1,4,6}, A ∪ B?

    {1,2,3,4,6}

  • A{3,2,7,6}, B{2,1,4,6,5}, A ∩ B?

    {2,6}

  • A{4,3,6,9}, B{7,8,5,4,6} A\B?

    {3,9}

  • A{1,2,3}, B{2,1,4,6}, B\A?

    {4,6}

  • A{4,3,6,9}, B{7,8,5,4,6} B\A?

    {7,8,5}

  • A{3,2,7,6}, B{2,1,4,6,5}, |A ∩ B|?

    2

  • A{1,2,3}, B{2,1,4,6}, |A ∪ B|?

    5

  • A{3,2,7,6}, B{2,1,4,6,5}, |A ∪ B|?

    7

  • E = ...

    Universal set

  • Ø = ....

    {}

  • if A is a set; P(A) = 2^A = ...

    {S | S ⊆ A}

  • A = {x}; P(A) = ...

    {Ø, {x} }

  • A = {x, y}; 2^A

    {Ø, {x}, {y}, {x,y} }

  • |2^A| = ...

    2^|A|

  • Â (Line above A) = ...

    {x | x ∉ A}

  • E={a,b,c,d,e,f},A={b,c}, Â=...

    {a,d,e,f}

  • Ê=...

    Ø

  • A ∩ E =... (Identity)

    A

  • A ∪ Ø =... (Identity)

    A

  • A ∪ E =... (Domination)

    E

  • A ∩ Ø =...(Domination)

    Ø

  • A ∩ A =...(Idempotent)

    A

  • A ∩ Â =...(Complement)

    Ø

  • A ∪ Â =...(Complement)

    E

  • A{x,y,z}; P(A)=...

    {Ø,{x},{y},{z},{x,y},{x,z},{y,z},{x,y,z}}