4) In this problem, we will explore how the cardinality of asubset S ? X relates to the cardinality of a finite set X.
(i) Explain why |S| ? |X| for every subset S ? X when |X| =1.
(ii) Assume we know that if S ? , then |S| ? n. Explainwhy we can show that if T ? , then |T| ? n + 1.
(iii) Explain why parts (i) and (ii) imply that for every n ? N,every subset of is finite and has cardinality less than n+ 1.
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