Let S be a set of n numbers. Let X be the set of all subsets...

Let S be a set of n numbers. Let X be the set of all subsets of S of size k, and let Y be the set of all ordered k-tuples

(s₁, s₂, , s_k)

such that

s₁ < s₂ < < s_k.

That is,

X	=	{{s₁, s₂, , s_k} \| s_i S and all s_i's are distinct}, and
Y	=	{(s₁, s₂, , s_k) \| s_i S and s₁ < s₂ < < s_k}.

(a) Define a one-to-one correspondence

f : X → Y.

Explain why f is one-to-one and onto.

(b) Determine |X| and |Y|.

\|X\|	=
\|Y\|	=

Expert Solution

Colby Messinger answered 1 year ago

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