Which term describes a function establishing a one-to-one correspondence between elements of two sets?

Which term describes a function establishing a one-to-one correspondence between elements of two sets?

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

Answer: (A)

A one-to-one correspondence between elements of two sets is called a bijection. It means every element of the first set maps to a unique element in the second, and every element of the second set is mapped from some element of the first. This requires two properties: injective (distinct inputs map to distinct outputs) and surjective (every element of the second set is hit by some input). When both hold, you have a perfect pairing between the sets. A function alone doesn't guarantee this; it might have multiple inputs mapping to the same output or miss some outputs altogether. That's why bijection is the term that describes a perfect one-to-one correspondence.

A one-to-one correspondence between elements of two sets is called a bijection. It means every element of the first set maps to a unique element in the second, and every element of the second set is mapped from some element of the first. This requires two properties: injective (distinct inputs map to distinct outputs) and surjective (every element of the second set is hit by some input). When both hold, you have a perfect pairing between the sets. A function alone doesn't guarantee this; it might have multiple inputs mapping to the same output or miss some outputs altogether. That's why bijection is the term that describes a perfect one-to-one correspondence.