If the statement ”Some birds are not mammals” is given as true, which of the following statements can be immediately inferred to be false?
Correct Answer :
All birds are mammals
Solution :
The correct option is: All birds are mammals.
To understand why this statement is immediately inferred to be false, we can use the traditional Square of Opposition from classical logic, which classifies categorical propositions into four types:
1. Universal Affirmative (A): "All birds are mammals" (All S are P)
2. Universal Negative (E): "No birds are mammals" (No S are P)
3. Particular Affirmative (I): "Some birds are mammals" (Some S are P)
4. Particular Negative (O): "Some birds are not mammals" (Some S are not P)
We are given that the statement "Some birds are not mammals" (an O-proposition) is true.
In the Square of Opposition, the relationship between A ("All S are P") and O ("Some S are not P") is one of contradiction.
Contradictory statements must always have opposite truth values. That is, if one statement is true, the other must be false, and vice versa.
Since the O-proposition ("Some birds are not mammals") is given as true, its contradictory counterpart, the A-proposition ("All birds are mammals"), must immediately and necessarily be false.
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