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1) How many subsets does a set A ={a,b,c...

1) How many subsets does a set A ={a,b,c,d} have?

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Prove that (i) if a set has only one element , then it has 2 subsets . (ii) If BsubA and if B has one elements less than that of A, prove that A has twice as many subsets as B . (iii) Deduce from these two results that a set with 2 elements has 2^(2) subsets , a set with 3 elements has 2^(3) subsets , and so on . How many subsets does a set with n elements have ?

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