If it is true that ‘all pollutants are harmful’, identify which of the following is invalid to infer from it?
[amp_mcq option1=”Pollutants constitute a subset of harmful things” option2=”No pollutants are non-harmful” option3=”If anything is harmful, it is a pollutant” option4=”Some pollutants are harmful” correct=”option3″]
This question was previously asked in
UPSC CAPF – 2011
A) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what “all pollutants are harmful” means. This is a valid inference.
B) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference.
C) If anything is harmful, it is a pollutant: This means “all harmful things are pollutants” (All H are P). This is the converse of the original statement “All P are H”. The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference.
D) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If “All P are H” is true (assuming there are pollutants), then “Some P are H” must also be true. This is a valid inference by subalternation.