Question

let A and B be two sets with m and n elements there is a bijection from A to B if and only if_______​

Answer 1

Answer:

•each element of X must be paired with at least one element of Y,

•no element of X may be paired with more than one element of Y,

•each element of Y must be paired with at least one element of X, and.

•no element of Y may be paired with more than one element of X.

Step-by-step explanation:

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Answer 2

A and B are two non-empty sets.

Let f be a function from A→B.

It is given that there is an injective map from A→B.

⇒ That means f is one-one function.

It is also given that there is an injective map from B→A.

That means every element of set B has its image in set A.

⇒ f is onto function or surjective.

If a function is both injective and surjective, then the function is bijective.

∴ f is bijective.