Corollary Meaning and Explanation

The term 'Corollary' refers to a statement or proposition that follows directly from, or is a direct consequence of, a previous statement, theorem, or proof. It's something that naturally arises from what has already been established.

Analyzing the Options for Corollary

Option 1: Something that is too expensive

This option relates to the cost or price of something. The definition of a corollary has nothing to do with financial expense. Therefore, this option is incorrect.

Option 2: Something that looks real but does not really exist

This description pertains to illusions, hallucinations, or things that are deceptive. A corollary is a logical truth derived from established facts, not something illusory. Thus, this option is incorrect.

Option 3: Something that naturally follows

This definition aligns perfectly with the meaning of a corollary. A corollary is a result or conclusion that stems naturally and logically from a preceding theorem or statement. For example, if you prove a theorem, a simple, direct consequence of that theorem can be stated as a corollary.

Option 4: Something resembling a coal mine

This option describes a physical appearance or similarity. The term 'corollary' is abstract and relates to logical connections, not visual resemblance. Therefore, this option is incorrect.

Understanding Corollary in Context

In fields like mathematics and logic, a corollary is often presented immediately after a theorem. It highlights an important implication or a simpler case that can be deduced without needing a separate, lengthy proof, because its truth is evident from the proof of the main theorem.