If it is true that ‘all pollutants are harmful’, identify which of the

If it is true that ‘all pollutants are harmful’, identify which of the following is invalid to infer from it?

Pollutants constitute a subset of harmful things
No pollutants are non-harmful
If anything is harmful, it is a pollutant
Some pollutants are harmful
This question was previously asked in
UPSC CAPF – 2011
The given statement is “all pollutants are harmful”. This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid.
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.
Understanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). The converse (All B are A) and inverse (All non-A are non-B) are generally not valid inferences.
In formal logic, this relates to the square of opposition and immediate inferences. The truth of a universal statement (All A are B) guarantees the truth of its subaltern (Some A are B) and its obverse (No A are non-B), but not necessarily its converse (All B are A) or contrapositive (All non-B are non-A), though the contrapositive IS valid if the original statement is true. In this case, the converse (C) is requested as the invalid inference.