The following problem, devised by Ginger Bolton, apeared in the January 1989 issue of the College Mathematics Journal (Vol.20, No. 1, p.68); Given a positive integer , let S be the set of all nonempty subets of . For each , let be the product of the elements of Prove or disprove tht
Prove or disprove that
Given information The following problem, devised by Ginger Bolton, appeared in the January issue of the college Mathematics journal : Given a positive integer , let be the set of all nonempty subsets of . For each , let be the product of the elements of .
Principle of mathematical induction is used to prove mathematical terms.
Let be the set of all nonempty subsets of for any positive integer .
Write the following statement :
For each let be the product of the elements of such that summation of product is given by the formula .
For and there is only single element of , namely .
That is, the product of all nonempty subsets of is .
Thus, is true.
Now, prove that for all integers , it is true, then is also true.
Therefore, in the inductive step, consider the set of all nonempty subsets of
Now, for , consider the set of all nonempty subsets of .
Now, any subset of either contains the element or does not contain the element
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