👉 Vacuousness is a concept in logic and mathematics, which refers to a property of statements that are false but cannot be proven true. It is often used in logical arguments to indicate that an argument has failed to establish any truth value or invalidity. For example, if someone says "All dogs have four legs," it does not follow logically that all dogs have four legs because the statement "All dogs have four legs" is false. However, if someone else says "There are cats with three