Step-by-Step Logical Analysis

To find the statement that is always true, we first need to simplify the two given premises into standard logical statements.

1. Simplifying the Premises

• Statement 1: "there are no dancers that aren't slim"
  This is a double negative. It means that if a person is a dancer, they must be slim. This simplifies to: "All dancers are slim."
• Statement 2: "no singers that aren't dancers"
  Similarly, this means that if a person is a singer, they must be a dancer. This simplifies to: "All singers are dancers."

2. Combining the Simplified Statements

Now we can form a logical chain from the two simplified statements:

All singers are dancers (from Statement 2), and all dancers are slim (from Statement 1).

By transitivity, we can make a definite conclusion: All singers are slim.

3. Evaluating the Options

• A. There is not one slim person that isn't a dancer. This simplifies to "All slim people are dancers." This reverses the relationship we found ("All dancers are slim") and is not necessarily true.
• B. All singers are slim. This exactly matches the conclusion we derived from combining the premises. This statement is always true.
• C. Anybody slim is also a singer. This means "All slim people are singers." This also reverses the relationship from our conclusion and is not necessarily true.
• D. None of the above. This is incorrect because option B is true.

Conclusion

The only statement that logically follows from the premises and is always true is "All singers are slim."