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.
- (a) P and Q only
- (b) Q and R only
- (c) P and R only
- (d) P, Q and R ✓ UPSC's answer
Why the answer is (d)
• The premises establish a transitive chain: Red ⊆ Blue, Blue ⊆ Green, and Green ⊆ Yellow.
• Statement P (Every blue is yellow) is valid because Blue is a subset of Green, and Green is a subset of Yellow, implying Blue ⊆ Yellow.
• Statement Q (Every red is green) is valid because Red is a subset of Blue, and Blue is a subset of Green, implying Red ⊆ Green.
• Statement R (Every red is yellow) is valid because Red is a subset of Blue, which is a subset of Green, which is a subset of Yellow, implying Red ⊆ Yellow.
• Since all three statements P, Q, and R are logically derived from the given premises, option (d) is the correct answer.
Why the other options are wrong
- (a) P and Q only
- This option is incorrect because it excludes statement R, which is logically valid as every red is ultimately a subset of yellow.
- (b) Q and R only
- This option is incorrect because it excludes statement P, which is logically valid as every blue is a subset of yellow.
- (c) P and R only
- This option is incorrect because it excludes statement Q, which is logically valid as every red is a subset of green.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.