Multiplicative Principle (in terms of sets): If X and Y are ﬁnite sets, then |X ×Y| = |X||Y|.
D) You are going to give a careful proof of the multiplicative principle, as broken up into two steps:
(i) Find a bijection
φ : <mn> → <m> × <n>
for any pair of natural numbers m and n. Note that you must describe explicitly a function and show it is a bijection.
(ii) Give a careful proof of the multiplicative principle by explaining how it reduces to the result of part (i). please write clearly
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