Which of the following is contrary to the statement "No mammals are birds"?
All mammals are birds.
Concept: In the classical Square of Opposition, two universal propositions with the same subject and predicate but opposite quality are contraries. The universal negative (E) 'No S are P' and the universal affirmative (A) 'All S are P' are contraries: they cannot both be true at the same time, though both could be false.
Working: The given statement 'No mammals are birds' is an E-type proposition (S = mammals, P = birds). Its contrary is formed by keeping the same subject and predicate but changing the quality from negative to affirmative and keeping it universal, giving the A-type 'All mammals are birds'. These two cannot be true together, which is exactly the contrary relation.
Why the other choices are wrong:
'No birds are mammals' is simply the converse of the original and is logically equivalent to it, not opposed to it.
'Some mammals are birds' is the particular affirmative (I); it is the contradictory of the original, not its contrary.
'Some birds are mammals' is a particular affirmative about the reversed classes and is the contradictory of the converse, again not the contrary of the given statement.
Takeaway: The contrary of a universal negative is the corresponding universal affirmative.
Correct answer: All mammals are birds.
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Important Questions from Classical Square of Opposition
Which of the following statements are so related that they can not both be true but could both be false?
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Which of the following statements are contradictory to each other?
A. All objects are perishable.
B. Some objects are not perishable.
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Choose the most appropriate answer from the options given below:
Among the following propositions two are related in such a way that they cannot both be true but can both be false. Select the code that states those two propositions.
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(b) Some students are attentive.
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