What is the negation of the statement:?

Question

"No slow learners take this course"?

could it be "All slow learners take this course" or perhaps "Some slow learners take this course"? How to find this out using mathematical logic?

Answer 1

Let S = slow learners
C = person who take this course.

Therefore, this translates into

No S are C.

The negation of this statement would be

Some S are C

Which translates into

Some slow learners are persons who take this course.
Or, simplifying the translation,

Some slow learners take this course.

By the link here:

http://en.wikipedia.org/wiki/Square_of_opposition

The square of opposition demonstrates negations of universal and existential quantifiers. It shows that the negation of
No A are B would be Some A are B.

Answer 2

Negations cannot both be true and they can't both be false either.

So "all slow learners take this course " is wrong because of only one took it, both statements would be false.

"Some slow learners take this course" is OK if some can mean all, but if some means "at least one but not all" then it is wrong too.

The best way to do it would be "at least one slow learner takes this course."

Answer 3

Some slow learners take this course.

"No slow learners take this course"? can be restated in if-then format:
"If one is a slow leaner, then one does not take this course."

One or more slow learners in the class would provide a counterexample and negate the statement.

Edit: Puggy is right, see below.

Answer 4

A negation always has the opposite truth value from the original statement. Therefore, you were right is saying, "All slow learners..."

Answer 5

the negation of statement A is NOT A
your statement can be rephrased to make this easier:

slow learners do not take this course

the negation is:

slow learners do take this course

because "do not not take this course" is eqivalent to "do take this course"
you might want to check out: http://search.yahoo.com/search?p=formal+logic&rs=3&fr2=rs-top&ei=UTF-8&fr=ush-ans