Expressing statements in Discrete math

Question

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.

$\begingroup$ $\exists a\in A:a\notin M$ $\endgroup$ – abiessu Oct 4 '15 at 1:43 — 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 — N. F. Taussig, Oct 4 '15 at 8:10

Jean-François Gagnon · Accepted Answer · 2015-10-04 01:58:07Z

2

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

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

answered Oct 4 '15 at 1:58

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$\begingroup$ 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

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Liam · Accepted Answer · 2015-10-04 01:58:27Z

1

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

i.e.

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

answered Oct 4 '15 at 1:58

Liam

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$\begingroup$ 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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2 Answers 2