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​If the statement - "All cows are herbivores" is given as true, then which of the following statements can be immediately inferred to be true?​
Question

If the statement - "All cows are herbivores" is given as true, then which of the following statements can be immediately inferred to be true?

A.

No herbivores are cows

B.

Some cows are herbivores

C.

Some herbivores are not cows

D.

All non-cows are non-herbivores

Correct option is B

"All cows are herbivores" (A-type)

We can immediately infer the following as true based on immediate inferences in classical logic (Square of Opposition and subalternation):

"Some cows are herbivores" (I-type)→True(Sub alternation: If "All S are P" is true, then "Some S are P" must also be true).

Information  booster 

  1. Contradictories (A-O, E-I):

    • Always opposite truth values(one true, other false).

    • Example:If "All S are P" (A) is true → "Some S are not P" (O) is false.

  2. Contraries (A-E):

    • Cannot both be true, butcan both be false.

    • Example:"All S are P" (A) and "No S are P" (E) can’t be true together.

  3. Subcontraries (I-O):

    • Cannot both be false, butcan both be true.

    • Example:"Some S are P" (I) and "Some S are not P" (O) can coexist.

  4. Subalternation (A→I, E→O):

    • Ifuniversal (A/E) is true, itsparticular (I/O) must be true.

    • Ifparticular is false, universal must be false.

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