Discrete Math - "No computer science students are engineering students" Struggling with a homework problem here and can't understand logically which one would be correct (each has different truth tables). I need to express the following statement using quantifiers, variables, and the predicates M(s), C(s), and E(s) 

"No computer science students are engineering students" 

D = set of all students
C(s) = "s is a computer science major"
E(s) = "s is an engineering student" 
So I'm stuck between,
$\forall s \in D, C(s) \implies \lnot E(s)$
-OR-
$\forall s \in D, \lnot C(s) \land E(s)$ 
 A: The first example says "All computer students are not engineering students".  People who are not computer students are free to be maths students or not be maths students.
The second one says "All students are not computer students and they have to be engineering students".
A: HINT:
For every student, his/her being a computer science student guarantees that they are not engineering students.
EDIT:
Your second logical statement claims every student is an engineering major and not a computer science major.
Your first logical statement is correct. But, do say if you see how this is so or if you would like further explanation.
A: 
"No computer science students are engineering students" 



*

*$\neg \exists s {\in} D ~(C(s)\wedge E(s))$ "there is not a student who is both".

*$\forall s {\in} D ~(\neg C(s)\vee \neg E(s))$ "all students are either not comsci. or not eng. student"

*$\forall s {\in} D ~(C(s)\to \neg E(s))$ "all comsci. students are not eng. students"

*$\forall s {\in} D ~(E(s)\to \neg C(s))$ "all eng. students are not comsci. students"

