If $A$ and $B$ are sets, and $A$ is element of $B$

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If $A$ is an element of $B$, then elements in $A$ are not necessarily elements of $B$.

Example: $A=\{1,2\}$, $B=\{\{1,2\},5\}$. In this case the elements of $B$ are $A=\{1,2\}$ and $5$, but $1$ and $2$ are no elements of $B$.

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Sumeet Chand
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Sumeet Chand

Updated on August 14, 2022

Comments

  • Sumeet Chand
    Sumeet Chand about 1 year

    If $A$ and $B$ are sets, and $A$ is an element of $B$ does this mean that every element of $A$ is in $B$, or some element of $A$ is in $B$, still makes $A$ element of $B$?

  • Admin
    Admin about 8 years
    You might want to change "elements in $A$ are not elements of $B$" to "elements in $A$ might not be elements of $B$"
  • Rohcana
    Rohcana about 8 years
    Or maybe use "elements in A are not necessarily elements of B"
  • Leox
    Leox about 8 years
    It is wrong: $A=\{1,2\}$, $B=\{\{1,2\},1,2\}$
  • This Is Me
    This Is Me about 8 years
    @JohnMa, Anachor, thanks, I indeed forgot the word "necessarily".