SME
Discrete Mathematics · Problem type
One-to-one, onto or both
Use this for “Is f(n) = 2n from ℤ to ℤ one-to-one, onto, both or neither?”
Sort
Is the function one-to-one, onto, both or neither?
Tap a card, then tap its group.
Assumptions
•
One-to-one (injective): different inputs always give different outputs.
•
Onto (surjective): every element of the codomain is the output of some input.
•
A bijection is both. The sets after the rule (ℤ → ℤ, ℝ → ℝ) are part of the function.
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Sets and functions
Main lesson
Power set and Cartesian product sizes
Use this for “A has 3 elements and B has 4. How many subsets does A have, and how many ordered pairs are in A × B?”
Counting functions
Use this for “How many functions are there from a 3-element set to a 4-element set, and how many of them are one-to-one?”