If the proposition ‘domestic animals are hardly ferocious’ is taken to be false, which of the following proposition/propositions can be claimed to be certainly true ? Select the correct code : Propositions : (a) All domestic animals are ferocious. (b) Most of the domestic animals are ferocious. (c) No domestic animal is ferocious. (d) Some domestic animals are non-ferocious.

If the proposition ‘domestic animals are hardly ferocious’ is taken to be false, which of the following proposition/propositions can be claimed to be certainly true ? Select the correct code : Propositions : (a) All domestic animals are ferocious. (b) Most of the domestic animals are ferocious. (c) No domestic animal is ferocious. (d) Some domestic animals are non-ferocious. Correct Answer (a) and (b)

Every categorical proposition can be reduced to one of four logical forms, named A, E, I, and O.

These are:

• A propositions, or universal affirmatives take the form: All S are P.
• E, or universal negations take the form: No S are P.
• I propositions, or particular affirmatives take the form: Some S are P.
• O propositions, or particular negations take the form: Some S are not P.

• The given statement:  'domestic animals are hardly ferocious' which means ‘domestic animals are not ferocious’ is taken to be false.
• So here, E propositions is taken False.
• As per the definition of Contrary Opposition: The two universal propositions—A and E, they can’t both be true, but they could both be false—though they needn’t both be false; one could be true and the other false. Therefore, All domestic animals are ferocious can be claimed to be certainly true.
• Also as per the definition of Subalternation: If an A proposition is true, it’s corresponding I proposition must also be true; if an E proposition is true, its corresponding O proposition must also be true. Therefore, Most of the domestic animals are ferocious can also be claimed to be certainly true.

Thus, the correct option is a and b.