Recurrence & Induction

(1) Demonstrate by induction on n the following property :

[ question in attached file]

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(2) Let E1 = {1, 2, 3, 4, 5} be the set ordered according to the following Hasse diagram (figure 1) :

a. / upper and lower bound of E1
b. / the maximums and minimums of E1
c. / the maximum and minimum of E1
d. / the upper and lower bound of E1
- Justify your answers by making the link with the definitions of the remarkable elements.


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