Which of the following statements is logically equivalent to the statement- "No saints are materialists"?

The correct option is: No materialists are saints

Step-by-step Explanation:

1. Analyze the Given Statement:
The given statement is: "No saints are materialists."
In categorical logic, this is an E-proposition (universal negative statement), which is of the general form: "No S is P" (where S = Saints, and P = Materialists).

2. Understanding the Logical Relationship:
The statement "No S is P" means that the set of Saints (S) and the set of Materialists (P) are completely disjoint. In other words, they have no elements in common.
Mathematically, this can be written as:
$$S���P=\varnothing$$

3. Applying Conversion (Logical Equivalence):
For E-propositions, the process of conversion is logically valid. Conversion is the operation of interchanging the subject term (S) and the predicate term (P) of a categorical proposition.
Since the intersection of two sets is commutative:
$$S\cap P=P\cap S$$
Thus, if no elements of S are in P, it logically follows that no elements of P are in S.

4. Evaluate the Options:
- Converting "No saints are materialists" by interchanging the subject and predicate gives: "No materialists are saints."
- This statement is logically equivalent and matches the correct option.