Examine the following statements: z 1) None but students are members of the club. 2) Some members of the club are married persons. 3) All married persons are invited for dance. Which one of the following conclusions can be drawn from the above statements?

Explanation:

Let's analyze each statement and option:

Statements:

1. None but students are members of the club. This means: All members of the club are students. (Club Members -> Students)
2. Some members of the club are married persons. This means there is an overlap: some individuals are both club members and married.
3. All married persons are invited for dance. (Married Persons -> Invited for Dance)

Evaluating the Options:

A) All students are invited for dance. From statement 1, we know club members are students. From statement 2, some club members are married. From statement 3, married persons are invited for dance. This means some students (the ones who are club members and married) are invited for dance. However, we cannot conclude that all students are invited. There might be students who are not club members, or club members who are not married, and we have no information about them being invited. So, A is incorrect.

B) All married students of the club are invited for dance. Let's consider a person who is a "married student of the club". According to statement 1, if someone is a "member of the club", they are a "student". So, "married students of the club" refers to individuals who are both "married" and "members of the club". If a person is a "married member of the club", then by definition, they are a "married person". According to statement 3, "All married persons are invited for dance". Therefore, any person who is a "married member of the club" (i.e., a "married student of the club") must be invited for dance. This conclusion can be drawn. So, B is correct.

C) All members of the club are married persons. Statement 2 says "Some members of the club are married persons". "Some" does not mean "all". There could be unmarried members of the club. So, C is incorrect.

D) None of the above conclusions can be drawn. Since option B is a valid conclusion, D is incorrect.

The final answer is B.