# Expressing statements in Discrete math

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.

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

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

i.e.

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

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