MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Let A and B be finite non-empty sets with ∣A∣=m and ∣B∣=n.
(i) State the condition on m and n required for the existence of:
(a) an injective function from A to B;
(b) a surjective function from A to B;
(c) a bijective function from A to B.
(ii) Give a reason for each of the three conditions stated in part (i).
(iii) For each of the three situations in part (i), write one explicit example of sets A and B (with m,n≤4) together with a function that satisfies the stated property.