All blue are colours and all colours are shades; which of the given conclusions about blue, colours and shades logically follow?

Introduction / Context:
This syllogism question deals with three sets: blue, colours and shades. Two universal statements relate these sets, and you must judge which conclusions follow logically if both statements are true.

Given Data / Assumptions:

• Statement 1: All blue are colours.
• Statement 2: All colours are shades.
• Conclusion 1: All blue are shades.
• Conclusion 2: Some shades are colours.

Concept / Approach:
We can interpret the statements as a chain of subsets: blue ⊂ colours ⊂ shades. That is, everything that is blue is a colour, and everything that is a colour is a shade. From this chain we can deduce transitive relations and existence of overlapping elements.

Step-by-Step Solution:
Step 1: From statement 1, every blue object is a colour. Step 2: From statement 2, every colour is a shade. Step 3: Combining these, every blue object is a colour and every colour is a shade, so every blue object must also be a shade. This proves conclusion 1. Step 4: Since colours form a subset of shades, and we assume colours exist, there must be at least some shades that are colours. Therefore conclusion 2 is also true.

Verification / Alternative check:
Take a simple example. Let the set of blue be {b1}, the set of colours be {b1, c1} and the set of shades be {b1, c1, s1}. Then all blue are colours and all colours are shades. Here, all blue elements (b1) are indeed shades, and some shades (b1 and c1) are colours. This concrete model matches both conclusions.

Why Other Options Are Wrong:
Option B claims only conclusion 1 follows and ignores the obvious existence of colours inside shades. Option C claims only conclusion 2, which is incomplete. Option D says no conclusions follow, which directly contradicts the transitive nature of the given statements. Option E suggests an either or situation, but both conclusions are clearly valid together.

Common Pitfalls:
A common error is to focus only on the first conclusion and forget to test the second. Another mistake is to treat some as meaning many or most, when it only means at least one. As long as there is at least one colour, there is at least one shade that is a colour.

Final Answer:
The correct evaluation is that all the conclusions follow from the given statements.