Which of the following statements are logically equivalent ?

1. Some animals are birds.

2. Some animals are not non-birds.

3. Some non-birds are not non-animals.

4. Some birds are animals.

Choose the correct answer from the options given below :

The correct answer is 1, 2 and 4 only.

Key PointsSyllogism:

• A syllogism is a type of deductive reasoning that involves two premises and a conclusion. The conclusion is drawn from the premises based on their logical relationship.
• A syllogism typically consists of a major premise, a minor premise, and a conclusion.
• The major premise is a general statement that establishes a broad relationship between two things.
• The minor premise is a specific statement that relates to the major premise. The conclusion is a statement that follows logically from the major and minor premises.

Important Points

• Statement 1 says "Some animals are birds," which means that there is a non-empty intersection between the set of animals and the set of birds.
• Statement 2 says "Some animals are not non-birds," is equivalent to Statement 1. It can be rewritten as "Some animals are birds," by using the double negation of "not non-birds" to mean "birds."
• Statement 3 says "Some non-birds are not non-animals," is not logically equivalent to Statement 1 or 2. It can be rewritten as "Some things that are not birds are animals," which is different from "Some animals are birds."
• Statement 4 says "Some birds are animals," is equivalent to Statement 1 because all birds are animals. It can also be written as "All birds are animals," which is logically equivalent to Statement 1.

Hence, the correct answer is 1, 2, and 4 only.