Answer
See step by step for answer.
Work Step by Step
(If there is a one-one function from $A$ to $B$, then $|A|\leq|B|$
Given: $A$ and $B$ are sets with $A\subset B$
To prove: $|A|\leq|B|$
Proof:
By the definition of a subset: If $a \in A$, then $a \in B$
We can then define the function f as:
$$f: A\implies B, f(a) = a$$
We need to check that the function f is one-to-one.
Let $f(a)= f(b)$.
By the definition of f , we then obtain $a=b$. Thus f is one-to-one.
Since f is a one-to-one function from $A$ to $B$ , $|A|\leq |B|$