Some mangoes are yellow. Some Tixo are mangoes. Based on these statements, consider the following conclusions: (i) Some mangoes are green. (ii) Some Tixo are yellow. Which of the following options correctly describes which conclusions logically follow?

Introduction / Context:
This is a classic syllogism and logical reasoning question. Two statements are given about mangoes, their colour and a group called Tixo. From these statements we must judge whether the conclusions about green mangoes and yellow Tixo necessarily follow. The key is to base the answer only on the given statements and not on outside assumptions or everyday knowledge about mangoes in general.

Given Data / Assumptions:

• Premise 1: Some mangoes are yellow.
• Premise 2: Some Tixo are mangoes.
• Conclusion (i): Some mangoes are green.
• Conclusion (ii): Some Tixo are yellow.
• We do not assume any information about mangoes apart from the two given statements.
• We do not assume that all mangoes are yellow or that no mango is yellow beyond what is stated.

Concept / Approach:
In syllogism questions, a conclusion follows only if it is true in every possible diagram or interpretation that satisfies the premises. The statement "some" means at least one and possibly more, but not all. The first premise says only that a subset of mangoes is yellow. The second premise says a subset of the group called Tixo overlaps with the group of mangoes. However, nothing in the premises connects the yellow mangoes directly with those mangoes that are Tixo. Likewise, nothing is said about green mangoes at all, so we cannot claim that some mangoes are green from the given information.

Step-by-Step Solution:
Step 1: Translate Premise 1: "Some mangoes are yellow" means there exists at least one mango that is yellow. Other mangoes may be of any colour; this is not specified. Step 2: Translate Premise 2: "Some Tixo are mangoes" means there exists at least one Tixo that belongs to the set of mangoes. We do not know its colour from the statement. Step 3: Consider Conclusion (i): "Some mangoes are green." The premises do not mention green at all. Mangoes could be yellow, red, green or some other colour, but since the premises are silent about green mangoes, we cannot say that some mangoes are definitely green. Conclusion (i) does not follow. Step 4: Consider Conclusion (ii): "Some Tixo are yellow." For this to follow, at least one Tixo that is a mango must coincide with the yellow mangoes mentioned in Premise 1. Step 5: It is possible that the Tixo mangoes are yellow, but it is equally possible that the Tixo mangoes are of another colour. The premises do not specify any connection between the yellow mangoes and the Tixo mangoes. Step 6: Since we can draw a diagram where Tixo mangoes are not among the yellow mangoes, Conclusion (ii) is not guaranteed and therefore does not logically follow. Step 7: As neither conclusion must be true in all valid interpretations, the correct choice is that neither (i) nor (ii) follows.

Verification / Alternative check:
Draw a simple Venn diagram with three sets: Mangoes, Yellow things and Tixo. Place some mangoes in the yellow region to satisfy Premise 1. Place some Tixo inside the Mango circle, but outside the yellow overlap, to satisfy Premise 2. In this diagram, no Tixo is yellow, so Conclusion (ii) fails. Also, the diagram does not force any mango to be green; their other colours are unspecified. Since we can construct such a diagram while respecting both premises, neither conclusion is logically forced, confirming that neither follows.

Why Other Options Are Wrong:
Saying that only (i) follows is clearly wrong because nothing is said about green mangoes in the premises. Saying that only (ii) follows assumes that Tixo mangoes are among the yellow mangoes, which is not guaranteed by the premises. Saying that either (i) or (ii) follows is also incorrect because we have shown a model in which both fail.

Common Pitfalls:
Many students assume that because some mangoes are yellow and some Tixo are mangoes, there must be some Tixo that are yellow. This is a classic error of assuming overlap between two overlapping subsets without proof. Another common mistake is to use real world knowledge about mango colours instead of sticking strictly to the statements. In syllogisms, always work with what is given and test conclusions against all possible diagrams that satisfy the premises.

Final Answer:
Neither conclusion (i) nor conclusion (ii) logically follows from the given statements.