Consider the following statements : Every red is blue. Every blue is green. Every green is yellow. Which of the following statements denoted by P, Q and R are correct? P. Every blue is yellow. Q. Every red is green. R. Every red is yellow. Select the answer using the code given below.

This question tests the principles of categorical syllogism and logical deduction, specifically applying the transitive property of subsets in set theory.

Why Option D is correct: Let us represent the given premises mathematically as subset relations:

1. 'Every red is blue' means the set of Red (R) is a subset of Blue (B): R ⊂ B.
2. 'Every blue is green' means Blue (B) is a subset of Green (G): B ⊂ G.
3. 'Every green is yellow' means Green (G) is a subset of Yellow (Y): G ⊂ Y.

Combining these premises yields a continuous chain of subsets: R ⊂ B ⊂ G ⊂ Y. We evaluate the given conclusions based on the universally accepted mathematical rule of transitivity (if A ⊂ B and B ⊂ C, then A ⊂ C):

• Statement P (Every blue is yellow): Since B ⊂ G and G ⊂ Y, it mathematically follows that B ⊂ Y. Statement P is correct.
• Statement Q (Every red is green): Since R ⊂ B and B ⊂ G, it follows that R ⊂ G. Statement Q is correct.
• Statement R (Every red is yellow): Since R ⊂ G (as proven in Q) and G ⊂ Y, it logically dictates that R ⊂ Y. Statement R is correct.

Because all three statements (P, Q, and R) are logically sound deductions, Option D is the correct answer.

Why the other options are incorrect:

• Option A (P and Q only): This option is incorrect because it fails to account for Statement R, which is a definitively true deduction.
• Option B (Q and R only): This option is incorrect as it arbitrarily omits Statement P, which logically follows from the premises.
• Option C (P and R only): This is incorrect because it excludes Statement Q, ignoring the direct transitive relationship established between red and green.

Concluding Takeaway: When dealing with continuous 'All A are B' (Universal Affirmative) propositions, visualize nested concentric circles. If set A is inside B, and B is inside C, the transitive property guarantees that A is entirely inside C.