Functions Ques 11
- Let $A$ and $B$ be two sets each with a finite number of elements. Assume that there is an injective mapping from $A$ to $B$ and that there is an injective mapping from $B$ to $A$. Prove that there is a bijective mapping from $A$ to $B$.
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Solution:
Since, there is an injective mapping from $A$ to $B$, each element of $A$ has unique image in $B$.
Similarly, there is also an injective mapping from $B$ to $A$, each element of $B$ has a unique image in $A$, or in other words, there is a one-to-one onto mapping from $A$ to $B$.
Thus, there is bijective mapping from $A$ to $B$.
BETA
