Given that

$A$ is the set of all Alpha's

$M$ is the set of all Men

how do I express this statement: Not all Alpha's are Men


My attempt:

$A \subset S = 0$

in other words saying that $A$ is not a subset of $S$, but I can't use the not subset symbol on this problem.

  • 1
    $\begingroup$ $\exists a\in A:a\notin M$ $\endgroup$ – abiessu Oct 4 '15 at 1:43
  • $\begingroup$ What is $S$? Did you mean $A \subset M = \emptyset$? $\endgroup$ – N. F. Taussig Oct 4 '15 at 8:10

You could write $A\backslash M\ne\emptyset$.

Meaning that when you take all the men out of the alphas, there are alphas remaining.

  • $\begingroup$ the \ is the difference symbol ? It makes a lot more sense this way, Thank you. $\endgroup$ – learnmore Oct 4 '15 at 2:10
  • $\begingroup$ Yes. It is equivalent to A\cap M^c. M^c being the complement. $\endgroup$ – Jean-François Gagnon Oct 4 '15 at 4:48

"not all alpha's are men" $\Leftrightarrow$"there is an alpha who is not a man".


$$ \exists a \in A \text{ such that } a \not\in M $$

  • 1
    $\begingroup$ I like the way you reworded it, makes it a lot more easier to express $\endgroup$ – learnmore Oct 4 '15 at 2:09

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