In this statement and conclusion based reasoning question, you are given two statements about bags, tables, and the colour red. Accept the statements as true even if they contradict real life, and then decide which of the given conclusions logically follow. Statements: (I) All bags are tables. (II) No table is red. Conclusions: (I) Some bags are red. (II) All bags are red.

Introduction / Context:
This question presents you with two statements involving bags, tables, and the property of being red. You must treat the statements as perfectly true for the purpose of the problem and then decide which conclusions are logically forced. The challenge is to track how being a bag connects to being a table and how tables relate to the colour red.

Given Data / Assumptions:

• Statement (I): All bags are tables.
• Statement (II): No table is red.
• Conclusion (I): Some bags are red.
• Conclusion (II): All bags are red.
• We assume nothing about bags or colours beyond what these statements provide.

Concept / Approach:
The first statement says that the entire set of bags lies inside the set of tables. The second statement says that the set of tables does not intersect the set of red objects at all. Combined, this means that bags, which are all tables, also cannot be red. Conclusions that talk about bags being red must therefore be checked against this restriction. A conclusion follows only if it is compatible with the statements in every possible interpretation.

Step-by-Step Solution:
Step 1: Draw a large circle for tables.Step 2: Draw a smaller circle completely inside the tables circle to represent bags, because every bag is a table.Step 3: Draw another circle for red objects such that it lies totally outside the tables circle, since no table is red.Step 4: Consider conclusion (I): “Some bags are red.” Since every bag is inside the tables circle and tables do not overlap with red objects, there cannot be any bag that is red. So conclusion (I) is directly contradicted by the combined statements.Step 5: Consider conclusion (II): “All bags are red.” This is even stronger and would require the entire bags circle to lie inside the red circle. But the bags circle lies inside the tables circle, and tables are completely disjoint from red objects. Therefore, it is impossible for any bag to be red, let alone all of them. Conclusion (II) is also incompatible with the statements.

Verification / Alternative check:
We can verify logically by simple implication chains. From statement (I), bag implies table. From statement (II), table implies not red. Therefore, bag implies not red. That is, no bag can be red. Conclusion (I) claims that some bags are red, which contradicts bag implies not red. Conclusion (II) claims that all bags are red, which is an even stronger contradiction. Since both conclusions conflict with the necessary implication bag implies not red, neither can be accepted.

Why Other Options Are Wrong:
Option A claims only conclusion (I) follows; this is clearly wrong because conclusion (I) states the opposite of what the statements imply. Option B claims only conclusion (II) follows, which is again impossible for the same reason. Option D suggests that both conclusions follow, which would mean we accept that some and all bags are red, which directly violates both statements. Only option C, indicating that neither conclusion follows, agrees with the logic.

Common Pitfalls:
Students sometimes get confused by the phrase “All bags are tables” and misinterpret it as “Some tables are bags,” then assume that some of those tables might be red. However, the second statement clearly prohibits any table from being red. Another common error is overlooking the effect of a “no” type statement, which creates completely disjoint sets. Whenever you see “No A is B,” ensure that the A and B sets do not overlap anywhere in your mental diagram.

Final Answer:
Hence, the correct decision is that neither conclusion (I) nor conclusion (II) follows from the given statements.