Question

Given below are two statements 1 and 2, and two conclusions I ans II.
Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the given statements and conclusions, which option is logically correct?

• A. Only conclusion I is correct
• B. Only conclusion II is correct
• C. Either conclusion I or II is correct
• D. Neither conclusion I nor II is correct

Hint:

When sets are only given as subsets of a bigger set, but nothing is said about their overlap, both overlap and disjointness remain logically valid.

Answer 1

The Correct Option is C

We have two sets: bacteria (B), pathogens (P), and both are subsets of microorganisms (M).

Step 1: Interpret the statements.
- Statement 1: \(B \subset M\)
- Statement 2: \(P \subset M\)
There is no information about the relationship between bacteria and pathogens. They may overlap, or they may not overlap.

Step 2: Check Conclusion I:
"Some pathogens are bacteria." This is possible because both are subsets of microorganisms. Overlap is allowed, but not guaranteed.

Step 3: Check Conclusion II:
"All pathogens are not bacteria." This means \(P\) and \(B\) are disjoint. This is also possible, since no information contradicts it.

Step 4: Logical evaluation.
Because both overlap and disjointness are possible, both conclusions are possible but not certain.
Thus, "Either I or II is correct" matches the logical interpretation.