As per square of opposition which of the following propositions are so related that if one of them is true, the other must be false and vice-vessa?

(A) All are vertebrates.

(B) No mammals are vertebrates.

(C) Some non-mammals are not vertebrates.

(D) Some mammals are not vertebrates.

Choose the correct answer from the options given below:

The correct answer is (A) and (D) Only.

To understand why this is the correct choice, let us analyze the propositions using the classical Square of Opposition in logic.
The Square of Opposition defines the relationships between four types of categorical propositions:

1. A-proposition (Universal Affirmative): "All S is P" (represented here by statement A: "All mammals are vertebrates" / "All are vertebrates").
2. E-proposition (Universal Negative): "No S is P" (represented here by statement B: "No mammals are vertebrates").
3. I-proposition (Particular Affirmative): "Some S is P" (e.g., "Some mammals are vertebrates").
4. O-proposition (Particular Negative): "Some S is not P" (represented here by statement D: "Some mammals are vertebrates are not" / "Some mammals are not vertebrates").

According to the Square of Opposition, two propositions are contradictories if they are so related that if one of them is true, the other must be false, and vice versa (they cannot both be true and they cannot both be false).
The contradictory relationships lie diagonally across the square:

• The Universal Affirmative (A) and the Particular Negative (O) are contradictories.
• The Universal Negative (E) and the Particular Affirmative (I) are contradictories.

In the given options:
• Proposition (A) "All are vertebrates" (Universal Affirmative, type A)
• Proposition (D) "Some mammals are not vertebrates" (Particular Negative, type O)

Since (A) and (D) represent a contradictory pair (A and O), they have opposite truth values. If one is true, the other must be false, and vice versa. Therefore, (A) and (D) Only is the correct relation.