What term describes a correspondence between two sets where each element of the first set is paired with a unique element of the second set and vice versa?

• A. Bijection
• B. Injection
• C. Surjection
• D. Function

Answer: (A)

A mapping that pairs each element of the first set with a unique element of the second set and also covers every element of the second set is a bijection. This means two things at once: it is one-to-one (different elements of the first set map to different elements of the second set) and onto (every element of the second set is the image of some element from the first). Because of this full, reciprocal pairing, you can always reverse the process with an inverse function. If the sets are finite, a bijection also implies they have the same size. A simple function doesn’t require both one-to-one and onto, an injection lacks onto-ness, and a surjection lacks one-to-one-ness, so only a bijection fits the described pairing.